Those are becoming a big problem for waste treatment plants. They've got several early steps in the treatment just to remove garbage before it gets to the digesters, that are only designed to handle organic material. Menstrual pads, condoms, trash of all sorts. The really big stuff gets filtered out with screens. Then it gets a bit agitated to break down the size of organic waste, and then goes through another smaller screen that tries to remove all the remaining non-organic material. Condoms and wipes are most of what it catches. That stuff btw is just loaded into a truck and hauled away to the landfill as garbage.
If you want a properly organic wipe, do what I do - keep a roll of soft paper towel by the toilet. (get the 'select roll' type, with the perforations every half-sheet) That's not so easy on the go, but works for me at home when I need to do some "cleanup". Paper towel biodegrades well and physically breaks down very quickly when submersed in water. It also goes down the plumbing easily. Wipes may be biodegradable, but they don't mechanically break down quickly, and will probably still be a firm square sheet by the time they get to the treatment plant.
