Oh, I was about to ask something really weird about pets. I do have an alt mage / scout (elf). I don't even know if this is related, but when I open my skills screen (K), I have 4 tabs instead of 3 and the last one is from pet. I don't recall seeing anything like it. My main is mage / druid / rogue(elf), and I have also priest / knight (human) and mage / priest (human). In all these chars I have a pet egg layed for crafting purposes but none of them shows this fourth tab. Since I'm at work now I don't have the SS to show, but I'll do it @night. Someone explain this?
as esccape said, the wd/x, p/x with the 50 elite, and m/s have a pet skills tab in their skill book. These are different from the pets gained by eggs and from the item shop pets.
There's some item shop or honor points items that convert training points to TP I think, but mostly you get TP from leveling your pet. Simply merge your pet with other pets of the same or lower level until you reach the next level. You'll then notice some points you can use to upgrade skills.
pets from eggs gain 100tp per an xp lvl, starting after lvl 10. I think it is actually lvl 5, but dont exactly remember, but know that I did not get the 100tp gain from the starting levels, 1-3.
The other way to gain tp for your pet is to feed it enhancement pots for each 500 training points the pet has. This gives 100tp for it.