As for removing labels from these bags, I’m afraid I must agree with other writers here - apart from label-stacking or painting over the bar code with a sharpie, there’s little you can do, the glue bond between label and bag is just so much sturdier than the bags themselves.
I haven’t used any of these flimsy bags in quite some time - but I am from a country where they are “questionable” (yay environmentalist parties) and stores must offer alternatives, either paper or reusable bags (scales with a tare function help).
That said, even before I got creative. My favorite method was to weight the items, place them in an old fashioned wicker basked and lightly stick the labels next to another either on the rim or the handle. Cashiers could easily check the contents of the basket (if items were placed in orderly clusters and not stacked), compare them to the stickers and run one sticker after the next over the scanner. I especially love that in combination with the self-checkout via smartphone scanner, because the produce gets handled less (just goes into the basket at the shop and in the fridge at home) and is packed properly and safely.
Caveat: This doesn’t work at self-checkout stations with scales, just saying. For those I have reusable bags or you could repurpose the flimsy ones, because there won’t be a cashier wondering about the stacks of labels.
Technically you will be paying just a tiny amount of extra money for the old labels (extra weight).