Working as a custodian, here's something I wondered about so I did a Google search. Here's one of the articles I found.
Apparently, it is better to put them in the regular trash if there isn't a green compost bin. Recycled plastic goes into making new plastic, or building materials such as Trex decking. The compost able cups are made from a different material that contaminates the plastic recycling process. Best to put composting cups into the compost able bin with food scraps, but if such a bin is not available, I guess the regular trash. Lots of people wouldn't know this.
Learning to be good at the game of creating a more usable waste stream. Intentional living. Here is a set of bins at Bellingham Food Coop with examples of what should go where. Still, the compost plastic is not mentioned. Here, it would go into the compost bin along with the fork and spoon which, in this case, are made from a special kind of cornstarch that can be composted. Most plastic utensils are not for compost. Many recycling stations don't have a compost bin. They only have recycling or trash. In that case, I would guess the compost plastic is better in the trash.