Good question @jtd1216! If this is for a temporary solution while replacing a door, one option is to exclude this sensor from your armed modes. In the Ring app, if you open the menu and tap "settings", you'll see"Mode Settings" as an option. Tapping on a mode (home, away) will give you the option to include or exclude specific sensors for that mode.
This means the Contact Sensor will remain connected to your system, but will not factor in to armed modes or emergency alerts. If you still want to completely remove that contact sensor, you can do so by visiting the Contact Sensor in your Ring app, tapping the settings cog in the top right hand corner of the page, and then selecting "Remove device" for instructions on completing removal. This Contact Sensor can certainly be added back to the system afterwards. I hope this helps!
I think you misunderstood the question @Marley_Ring. Can we CLEANLY remove and reinstall the contact sensor? I'll put it another way: Can we move the installed contact sensor from one place to another? If so, how do we do this?
Glad to have read your instructions for the settings during the removal process!
If you are asking can you simply physically move the sensor to the new door, my recommendation is to not use the tape but screw it on.
That way you can just open the sensor, unscrew it and then place on the new door. On the new door I suppose you could tape it if you desire. I say tape, use the included sticky pad.
The tape included is quite tacky (for good reason) but will likely leave a residue, or rip the paint off if peeled forcefully. I have decided to use instead 3M Command strip tape to hold the sensor in place. These have really good sticking power but can be more easily removed without damaging wood/paint.