The tank holes are threaded (at least on my 05).
The fender emblem is stuck on with adhesive and also has two little slip on retainers over plastic tabs on the trim inside the fender, both sides of the trim have this on it's toward the ends.
It can be a ***** to get these off.
Once you have those off, use some 3M Adhesive remover and waxed dental floss on the front Triumph badge. There's a screw under it, remove that screw.
If for some reason there is no adhesive holding the rest of the trim on, it will just fall off, if there is, do the dental floss/adhesive remover trick.
Don't forget to rewax when you're done, the adhesive remover will strip any wax you have on there off.
I could be wrong on that front screw, it's been awhile since I pulled mine and I can't remember which way it goes (from the rear (tire side) to the nut or from under the badge to the nut, check it out before pulling the Triumph badge though)
Skip, on the tank emblems, all you need is th remover and the floss. Spray the remover above the tank emblems so it runs under them and into the stick'um. Let it sit for a few minutes and take the waxed floss, slip it under the front of the emblem and "saw" it back and forth while pulling toward the rear. Once you get to the first tab on the back of the emblem, you'll have to lift it a bit to get the floss under it. Once past the first tab, keep sawing back to the second, lift the emblem up again, saw away all the way to the back edge of the emblem and it's off.
Spray some more adhesive remover on the tank to clean up any stick'um left over. Spray down the whole tank to pull all of the wax off and then rewax.