Polyethylene is very easily recycled so I would hope the grocery stores are doing the right thing with them. In fact, this place I work for has a bin for employees to bring in grocery bags from home. They also get as many as they can from local businesses, one of which I know is a grocery store. They grind them up, melt them down, form them into new plastic resin beads and process them into bags. Colors are an issue so this place makes and sells 33 and 55 gallon trash bags in varying shades of grey to brownish grey. Heavier in mil thickness than anything you can get from the store.
The reason this small company has the recycling equipment is to recycle all their own scrap which can amount to 1,000s of pounds every month. Most of it is simply trimmings, not mistakes. Typical scrap rates are 5-7% of the new plastic film produced. Pretty sure most plastic film/bag makers do the same.
Don’t feel for a minute that you need to explain/justify any of this to me! :)
As Madonna sang so long ago, ‘We are living in a Material World and I am a Material Girl.’ ;)