After sending my MacBook Pro out for repairs, I got it back as a factory reset, so I had to go through the process of restoring from my Time Capsule. After completing the restore, there's now a new "Reset Password" button on the login screen that I swear wasn't there before. I'm afraid to click the button and mess things up, so I just want to know: if someone were to get a hold of my laptop and click that button, would they have to enter the current password before they could reset it? It makes me nervous that that button is there. How do I get rid of it?
You should push the button and set the password to whatever you like.
Since the machine was "factory reset" (as per yours) and then you dropped the TM backup on top of the reset, she/he/it now has non-matching credentials and is asking you to set things right.
Do all this under the usual precautions: own risk, make sure your backup is good and usable in case you have to repeat the process, etc.