My 2007 Fit automatic makes this sound on cold starts. Anybody know what it could be? Thanks!

 

If it's a manual transmission it's the bendex gear within the starter module going bad. Had this happen on my Accord and it's also happening on my Fit.

As far as I know, it won't hurt anything (except the starter itself) so take this chance to order a replacement, and just wait until it completely fails to replace.

Edit: BTW when it completely fails you'll get nothing when you turn the key. Not even insufficient power clicks like when your battery is dead. In my Accord it was intermittent and I could get it started if I waited a few minutes.

 

Starter (lubricant in the planetary gear) and/or solenoid
I've replaced solenoid and lubricated gear; waiting for cold temperatures (if will not succumb to covid-19)