"Back in your gilded cage, Melanie Daniels," says Mitch in the pet shop.
Cages and cage imagery are everywhere in the The Birds. Not surprising for a movie about birds, we guess, but most of the birds have no intention of being caged like the ones in the pet shop. The lovebirds stay in their cage throughout the film, and it's the humans who end up being locked up.
Think about it.
In their homes, in the diner, in cars—Hitchcock gives us lots of shots of people confined and trapped like birds in a cage:
We see Cathy framed through the window after Annie has been killed.
Melanie gets her own private cage when she has to hide in the phone booth from the melodious marauders.
And, as Hitch pulls back for the "God shot," the bird's-eye view looking down at the chaos, we see that the people are trapped wherever they are. They can run, but they can't hide.
Some people have interpreted the cage imagery as representing a sense of personal confinement. Here's what critic Gus Cileone says:
Even for an heiress, it can be difficult to escape the life one inherits, if Melanie's is an affluent (and many would say enviable) cell. Mitch, on the other hand, is a lawyer who admits to wanting to put people in jail. This conversation between the two (not conventionally likeable) would-be lovers immediately establishes the theme of human preoccupation with possessing, controlling and confining. (Source)
Cileone goes on to speculate that the characters have incarcerated themselves in dysfunctional family situations that trap them in a tense web of relationships.
Whether or not you buy that interpretation, the humans are sure trapped physically. The airborne assailants have clipped those humans' wings and taken away their freedom of movement. It's tempting to think of it as payback even though we know that's not really the case. But honestly, we would've let those lovebirds out of their cage in a nanosecond once the mayhem started.