Plastic bags separated from other trash/recycables brought to the store wouldn’t be much of a problem for Kroger. I don’t think consumers would bother unless a deposit was involved.

In my state, grocery stores literally do take plastic bags back, they have standardized drop off bins and everything.

And I have read accounts that some of those stores simply toss them into the garbage in the back.

Plastic film used to be recycled specially where I live. They stopped doing that because there was no market.