You can delete a constraint from the list of constraints in the model
You can list them with model.Proto().constraints
Note that the list is ordered based on the order you added the constraints to the model, so I would suggest you to log somehow the index of the constraints every time you add them
Note also that if you use Interval variables and not one of the last version of ortools, some "hidden" constraints are added to the model, so that each time you use AddIntervalVar, two constraints are added in the list
Once you have the list of constraints, you can manipulate them popping one or more of them from the list and then solve the model