the probe between the glass and UTH is to keep the temperature as consistent as possible with no variables to change it. placing the probe inside the tank has too many variables which can change the temperature reading: poop/urine, water, snake pushing substrate around, etc. if you're veeeeeeeeerrrrryyyyyyyy careful, you can pull the UTH off and maybe reapply it; i used to have a UTH like that but the instructions say not to pull it off and reuse it because you can damage the internals and it can mess up. however if getting another UTH isn't possible you can try and pull it off, maybe use aluminum tape to hold it into place if its lost its sticky-ness.
you could also try to just lift up a section of it and slip the probe in, and use aluminum tape to keep everything in place. again, be very careful when pulling on the UTH.