Hi guys, 

So I bought a used FMT HH Telecaster quite a while ago on eBay. It came with some damage — a couple of screw holes and some glue residue where I assumed the previous owner had had a Bigsby installed. I had always planned to find the same model in order to address the damage. I could use a Bigsby, afterall, and doing so seemed like it would surely be the easiest solution.

Well, the trouble I'm having is that the location for the glue residue is pretty puzzling and doesn't line up at all with where any sort of trem I can find would possibly be located. I mean, it just has nothing to do where you'd imagine it would be.

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So I ask thee, internet, what was there? Any ideas? Thanks.
It was a sticker. Somebody put a band sticker on there years ago, and then when they went to sell the guitar they gouged the shit out of the top trying to get it off, and the residue remains. 

Sad story, no trem involved. Pretty common. 
Roc8995 what about the screw holes though? there's two close to each other by the glue residue, plus another two on each side of the strings near the bridge.
Interesting. They just looked like gouge marks to me, as if someone had really screwed up trying to scrape the sticker off. I missed the ones by the bridge. 

All of those screw holes are smaller than what you'd use to mount most trems. The ones by the sticker residue are so far off-center they can't possibly have been used for a trem system. Even the ones near the bridge aren't exactly lined up right. I wonder if someone was trying to attach something to the top (large pickguard, some sort of faceplate with electronics, a kaoss pad perhaps) and used adhesive and screws to do it. 

I really don't think it's a trem, but the screw holes are odd and I'm not sure what to make of them. It was clearly not a professional job, whatever it was. 
Roc8995 Gotcha. Thanks for the answers! 

While we're on the topic, if I wanted to maximize the guitar's resale value by covering the glue residue up with something, would you have any suggestions? Interested in the idea of mounting a kaoss pad or perhaps some other electronics/pedal but I don't have a lot of experience with that.
I wouldn't bother. You're going to spend more on a competent installation than you'd gain in value. 

Someone with finishing experience might be able to touch up those screw holes, at least so they're not visible from far away, but usually with sticker gunk the best you can do is remove it as best you can. Someone who knows what they're doing might be able to clean that up a bit, too. Be careful, though, it's not hard to make things worse. An amateur job might be worse than nothing, and a decent fix may well cost more than you'll gain back in resale. 

With a guitar in this price range there's a fairly low limit on how much resale value you're going to recoup. 
There is no glue associated with a Bigsby. At least not any of the three guitars I have with a Bigsby and I can't imagine where any Bigsby would need glue. The screw holes are a mystery. They don't make any sense are in such an odd place. 
Yes I am guitarded also, nice to meet you.