I'm a Dummy, Tell Me About Turntable Mats


Turntable mats seem to be an inexpensive way to improve a component, but the thing that gives me pause is that as I understand it, you put them on with adhesive. Is there a possibility that a turntable would be damaged by a turntable mat?

If it's relevant at all, the turntable I'm thinking of using a mat on is a Sota Comet III bought used.
heretobuy
I knew there would eventually be the usual opinions here. I have one. 96.73% of the time they change the sound but don't improve it. I always wondered if HW was having a little fun at the expense of the rubes when he added a piece of very thin brown parchment paper as a platter mat with his decks. Platter mats, periphery rings and center weights all change the sound. Mats the most, periphery rings the least, center clamps/weights in the middle. Once your ears and brain become accustomed to the change they don't add anything to ultimate enjoyment. This is not what most vinyl enthusiasts want to believe, so they won't. 
The biggest benefit of platter mats is to enable those with VTA/SRA problems-those that can't go low enough-to achieve proper VTA/SRA. I think Herbie's caught onto this. 
OP i would ask Donna at SOTA if you have the latest mat on your TT. i find the new mat they provide w Sapphire to be excellent w Reflex clamp.
@lewm, it is not an echo. It sounds like a very high frequency copy of the music. What is vibrating can not emit anything from maybe 6 kHz down. I'm just guessing. With the vacuum engaged I can just barely make out cymbals. With the record loose it is 2X louder and I can make out a little more. It is still very quiet. You have to put your ear next the rim of the record to hear it. I remember my old Zenith which I got when I was 4 years old. I use to marvel how I could hear the music with the volume turned down. It was pretty loud. You could hear it across the room. 
Remember the old Victrolas? They had a sowing needle in a shank fixed by a grub screw. The shank was attached to a diaphragm in the throat of a horn. Same thing but no diaphragm or horn. You are hearing whatever is vibrating. The less you hear the better is the control over distributed resonance from the stylus and cantilever vibrating. The cavity around the stylus can act as a horn which is why many manufacturers stick the cantilever out in thin air. That resonance is reflected back at the cantilever to be heard. You really only want to listen to the record. Nothing else.

The best record playing set ups hardly make any noise at all. There may be a few out there that make no noise at all. I have never heard one make absolutely no noise but I have heard a few get very close. 
Just don't laugh when you see a guy with a tonearm stuck in his ear. 

The point of all this is, the job of a turntable mat is to help control resonance. It is to help keep the record from vibrating under the stylus.
Because records are not flat a mat can not do it alone. People figured that out and started using record weights, then record clamps, then taking a lesson from record lathes, vacuum clamping. I am comfortable with saying that vacuum clamping is overall the best. I do not know if it sounds better than reflex clamping but it does results in the best control over the record with the least effort and stress on the record. 
If your definition of record noise is “a high frequency copy of the music” then we’re probably both talking about the same phenomenon. I find it varies in audibility in relation to cartridge output voltage magnitude. I have always felt it comes with the territory, and I pay no attention to it, because my listening seat is far enough away from the turntable that I never hear it while I am trying to concentrate on what is coming out of the speakers. What’s the big deal?