I would consider adding the tag access=private (more detail here https://wiki.openstreetmap.org/wiki/Key:access). If you want to dig deeper and set hours for when it might be acceptable to walk through there, you could probably accomplish that with a conditional restriction https://wiki.openstreetmap.org/wiki/Conditional_restrictions but then the problem is "does CoMaps respect conditional tags". I don't know the exact answer to that, but my AI slop answer is that it should respect access=private, but if you make it conditional (add times, etc.) CoMaps won't respect those limits.
If I'm looking at the place you're thinking of, the route that goes through the school yard is of the type "driveway". Since you're familiar with that area, you could keep it as a driveway or change it to something more accurate.
Keep in mind once you update OSM, CoMaps will only include it during their next cycle which I think corresponds to app updates.