Time Machine won't let me select any previous backups

Had a problem with my 2014 Mac Mini's disk, so after chatting with Apple, I took it to the Genius Bar, where they did some checks, and deleted my hard drive, leaving it with just the MacOS 10.12.6 installed. The guy recommended restoring files individually, and not the wholesale Time Machine restore. I went home and hooked it up to my backup disk and fired up Time Machine. I can see previous backups in the usual way, but it doesn't let me select anything. The scale at the right slides up and down, but the Finder window doesn't move off "Now".

I suspect this is related to the fact that it looks like a different computer now (different name) from what it was when the backups were generated.

Any suggestions?