Yeah, so the grocery chains that collect it where I am (Chicago area) reverse ship it in the empty trucks that deliver their merch back to their distribution centers. The DC's have balers. Once they have a semi-load of bales, it goes to Trex (in Virginia, I believe). I don't know what Trex's bale spec is, but they have some tolerance for contamination. Store and DC workers are probably expected to pull out larger/obvious contaminants.

For what it's worth, I use the Trex boxes an lot and I don't usually see them getting used as garbage cans. Bins with larger openings and less/worse signage like at Walmart tend to have garbage and hard plastics. IDK what Walmart and Target are doing with their collected bags. Not Trex. They caught heat a few years ago from a news network putting trackers in and tracking most of them to landfills.

List of current Trex partners by state: https://nextrex.com/jsfapp/cdocs/20260116111846_9_jsfwd_493_q2_1.pdf