Please find more information here.
I assume this can be done. I know that there are a couple different reset choices. However, I think reset removes existing programs? So if that is the case, wouldn't I lose connection with the remote pc?
Do you mean reset to factory settings? If so this is not possible because when you activate the reset its going to delete all the file's and programs (aslo teamviewer). So you don't have a connection anymore and you'll need to set some settings in the reset and after the reset...
I hope this helps,
Thank you for using teamviewer.