At this point, separating the coin from the letter is going to damage the letter - Something I'd rather avoid if it were me. Having the coin and the letter together is good for the provenance of the coin in some ways.

I'm not sure I'd even want to have that graded, especially over something like an FDI label - something I'm not sure they could even give you without breaking their own rules for the label because they do FDI based on the date something was shipped from the mint and they have cut-off dates for them on everything. While the FDI label gets attention with some people in the moderns market for coins issued in the last 10 years and some people pay more for them - in part because, at various points in time, NGC has given more registry points for FDIs, giving registry users an incentive to go after them and QVC hucksters like to pump it up. But I don't really see the FDI label adding any value to something like that.

Just my $0.02. Completely up to you though on if you want to submit it for grading.

https://money.org/collector/drdarryl/blog/the-unsung-first-day-issues The Unsung First Day Issues blog at the ANA

I'd leave that exactly as it is.