I purchased this coin raw in 2013, sent it in for grading, looked at it several times and never realized the error on the slab until now...do you?
$20 should be $10 dohhhh. I think they would fix it for free. First check the verification on this coin first. link: https://www.pcgs.com/Cert/24702318/
It's a mechanical error which they will fix for free, just call customer service. They may ask you to send them a picture so they can create a shipping label and stuff.
I'd be inclined to leave it as is, just for the curiosity factor. When I see errors like this, it makes me wonder if there's a $20 Saint out there with your label...and if that labels says 1926 $10 MS65.
Usually can check the cert 1 lower and 1 higher. 1 lower is another double eagle, but 1 higher is invalid. So whomever got the $20 marked as a $10 has probably already returned it...
At least no one has suggested that slab errors themselves increase the value. That would be as silly as say, collecting used Clove Gum memorabilia, paying more for the empty gum wrapper than the actual chewing gum. Uh, oh. Wait.
You might crack it out and see if NGC returns it with the same doubled face value error. If it does, it opens up a huge new market...
Surprise, the Saint before the certification number of the 10 $ piece is mine as well. Both were part of the same submission.