Handling 'Transaction count after EXECUTE indicates a mismatching number of BEGIN and COMMIT statements'
Is there any way I can catch and handle this error?


No.  This isn't your problem.  You have some other error, and your stored procedure is coded to rollback on error.  Performing a ROLLBACK in a stored procedure that didn't start the transaction is also an error, and will generate this message.

You need to look at the previous error.  Before the ROLLBACK the procedure should be calling RAISERROR or THROW to return the underlying error details to the client.  In SSMS you'd see both error messages, in Visual Studio debugging the SqlException has a collection of Errors you can interrogate.  But other clients sometimes only display the last error message.

If it isn't, it should.  Also you can use Profiler to see it regardless, using the "Errors and Warnings"/"User Error Message Event" or similar XEvent.