I was cleaning my car's tires and I notice they say "130 MPH rating". Oh no! I only drive 70 mph! Do I need to get the tires changed? Where do I even buy 70 mph tires?
That's what you're talking about there. You have a subpanel that is rated 100 amps maximum. You are actually sending 50 amps through it. That is allowable and safe, because 50 < 100.
The THHN wire is #6, because the installer was a dummy. But you can take advantage of that. #6 THHN is actually good for 65A. Back at the main panel, this can be fed by a breaker as large as 70A (65A, rounding up to the next existing breaker size).
Inside this panel are several things.
First, there's a 50A GFCI breaker already in it. That's designed to feed 50A to a hot tub. And by wild coincidence, YOUR hot tub is 50A, and it needs a GFCI breaker! So yeah. You can reuse this GFCI breaker. And since they're $100 normally nevermind COVID shortages, that's a good idea.
Second, there are 2 empty spaces in this subpanel. Each space has 15 amps to spare. You can install 240V-only loads: continuous loads up to 12 amps, or non-continuous loads up to 15A. So for instance a well pump could go there.
Third, it really looks like the dummy who wired this chose to cut off strands of the wire to make them fit on the bars. That neutral bar ought to be able to take #6 wire just fine. So clean that up.
Fourth, this panel doesn't have neutral brought from the main panel. Nothing here uses neutral except the GFCI (to power itself), and that is bootlegging neutral from ground. That's not how I would've done it, but I'm not going to tell you it's unsafe. If you want anything in this panel that uses neutral, you will need to pull a neutral wire from the main. To make space in the conduit, change out that #8 ground (amateur!!!) to a bare #10 ground. Also, remove the neutral-ground strap and install an accessory ground bar, so grounds are separate from neutrals.