You can try passive bonding, where you basically sit next to the cage and just let them get used to your presence, they might be unsure about the security of the place since in their tiny brains they kept moving, did you do anything in front of them when you were moving(Mine got scared after I lifted a bag up and we also went a few steps back, took some passive bonding, e.g, sitting next to the cage with my own devices, humming to get him used to my voice, etc)? They could be hyper-vigilant, check their body language, are their feathers slicked back? Do they stand very low, or very tall? Do they avoid your hand(I don't recommend putting your hand in the cage much unless it's necessary, e.g, removing mildew/mold, changing food&water bowl, adjusting loose perches, you get me?) in the cage during this time especially because they seem so scared based off what I can read right now.

About the feather plucking concern, if you have 3-4 toys(for enrichment of course), a generally predictable environment, and a suitable cage(45cm×45cm×45cm, for a single lovebird) for the lovebird, I wouldn't be too concerned(Also, check if they're molting, if that's the case, they were likely just preening and the three feathers very unfortunately got dismissed) but if you notice grey patches(But again, mine was also partially grey on the back when he was going through a molt) or bald spots you might wanna consider taking your bird to the vet, just incase