We often see Hera punishing Zeus's children or the mothers because of her jealousy. But such is not the case with the hero Perseus or her mother. She isn't even mentioned trying to cause any harm to them (that I have thus read). Why is that? What doesn't Hera antagonize Perseus as she did Heracles, Leto, Io, Echo, Semele, Dionysus and many other?
Yes, she did know.
There is no ancient source (that I know of) in which Hera seeks to harass Perseus or his mother Danae. There is, however, a mediaeval Latin text called the First Vatican Mythographer which records a rather different version of the story of this hero and his mother, in which Hera does in fact go after Perseus out of jealousy that Zeus is looking out for this illegitimate offspring of his.
In the commonest rendition, when Perseus is born, his grandfather Acrisius puts him and his mother in a wooden chest which he casts into the sea in the hope of killing the little boy (who at this point is either a newborn or up to four years old). The chest finds its way (via divine intervention from Zeus, according to Hyginus) to the Cycladic island of Seriphos, where the local fisherman Dictys takes care of Danae and helps to raise Perseus.
According to the Vatican Mythographer, while Danae was still pregnant, Acrisius placed Danae on a ship rather than in a box, "to go where chance would take her. Through the mercy of the gods she was carried to a safe place, namely, Italy."✭ There she was found by a fisherman named, confusingly, Perseus. Shortly afterwards, she gave birth to "and named her son Perseus", presumably naming her child after the fisherman.
At this point, Jupiter [the Roman Zeus] gets involved in a way he never does in the better known forms of the myth:
Jupiter entrusted Perseus to a certain king to be raised. Pained by this, Juno [Jupiter's wife, the Roman Hera] was filled with unspeakable hatred. She decided to persecute Perseus and urged the king to destroy him somehow. The king sent Perseus to slay various monsters...
From other references to Perseus in the Vatican Mythographers we know that the hero survived his ordeals against these monsters.
The placement of Danae and Perseus in Italy is not completely out of left field, though. Juno's persecution of Perseus might not be derived from a genuinely ancient myth tradition (it seems to be modelled on Hera's persecution, rather, of Perseus' descendant Heracles, who is yet another one of Zeus's mortal indiscretions); nonetheless in Virgil's Aeneid, the box into which Acrisius casts Danae floats to Italy, where she marries a local king named Pilumnus and becomes an ancestor of Aeneas' rival Turnus. In Servius' Commentary on the Aeneid, she even ends up living on the spot upon which Rome is later founded.
Hera's Awareness in Older Mythography
As for actual ancient sources, there are at least two of them which make it explicit that Hera knew Perseus's paternity. The first is Nonnus' Dionysiaca, which places the reign of Perseus in Argolis during the time that Perseus' half-brother the wine-god Dionysus is concluding his epic tour of Greece. At the end of Dionysus' itinerary is the region of Argolis, one of whose major cities is Argos, partly ruled over by Perseus' relative Melampus.
Argos is famously known as a city dedicated to Hera. Centuries before Perseus and Dionysus were born Poseidon and Hera had contended strongly for the honour of becoming the city's patron deity, and Perseus' ancestors had awarded Hera the position. In Dionysiaca 47, by the time that Dionysus comes with his campaign entourage to Argos, the notoriety of Hera's hatred of him is so widespread that the Argives are fearful of a reprisal from their goddess if they receive this enemy stepson of hers. The citizens therefore turn Dionysus' army away from their home, which then provokes a retaliation by Dionysus, who induces madness in the city's women so that they start to butcher their own children.
This in turn attracts Hera's attention, who swoops to the aid of her city by disguising herself as Melampus and, in this form, goading Perseus into defending Argos against Dionysus' attack. In the fight that ensues, Dionysus' new bride Ariadne gets turned to stone by Perseus, who achieves this by using the deadly head of the slain Gorgon Medusa. An enraged Dionysus is then ready to destroy the city as well as other parts of Argolis, threatening to annihilate the land's inhabitants, at which point another half-brother, the messenger-god Hermes, appears behind him and convinces him to cease fighting, explaining that Hera, who is involved in the battle, possesses the power to defeat him.
With Hermes' help, Dionysus and Perseus afterwards become friends while the real Melampus establishes the cult of Dionysus in Argolis. The wine-god then moves on from there to Thrace to conclude his adventures in the final book of the Dionysiaca.
~ from my Answer to another Question
In the speech used by the disguised Hera to stir Perseus up in defense against Dionysus, she references the conception of Perseus by his mother, urging Perseus to:
remember the bronze vault which was Danae's chamber, where Rainy Zeus poured into her bosom a shower of bride-stealing gold—let not Danae, after that bed, after the wedding of gold, bend a slavish knee to that nobody Dionysus. Show that you have in you the true blood of Cronion [Zeus], show that you have in you the golden breed, proclaim the bed that received that snowstorm of heavenly riches... Why do you tremble before Dionysus, no offspring of the bed of Zeus?
The play Hercules Furens, by the Roman writer Seneca, opens with Juno listing a number of Jupiter's indiscretions with other women and how different aspects of these illicit unions are celebrated across the sky itself in the form of constellations. In the case of the Gorgon-slaying hero, after his death, Zeus made him into the constellation Perseus.
Juno refers to the women in her catalogue here as harlots, bearing a clearly much less flattering perspective than the one presented by Nonnus. Granted also that Hercules Furens proves only that the goddess in question is aware of Perseus' paternity long after he has died, a few generations in fact.
✭ This and all other quotes of the Vatican Mythographer in this Answer taken from Ronald E. Pepin's translation of The Vatican Mythographers (numbered as First Vatican Mythographer 154 [pp. 71-72], published 2008, Fordham University Press, New York).