Unlikely, as long as you cut off any non-postage-related barcodes. But normally the label just has barcoded address information and the “business reply mail” postage permit number.
I like to just mail the letter they sent me back to them in the envelope they sent, usually with a stick so it doesn't bend and costs more due to hand sort
You don't have to be an ass to the wage slave opening the return mail, but you can still send them a message. Print out joblistings for the return address area and return them. Maybe add a few Bible quotes. But make sure you are remembered by getting a stack of sassy stickers from temu and putting a few in there as a little gift.