No, it will not damage your LED. Think of Protected cells as having a govenor on the throttle of an engine. The protection device in the battery will only let so many amps out of the battery at once and will only let you discharge it down to a certain level. If you put an unprotected cell, say a 30Q like I use, in your TK20r it will work great. Just make sure to read up on lithium battery safety so you know what you are doing.
As a general rule, you will not need high drain cells (like the ones you mentioned) for off the shelf lights.
Think of your battery being like a bath tub. The number of mAh (say 3000mA on a 30Q) is how much water the tub holds, the cells capacity. The cells Amp rating is like how quickly you can drain the tub. A "high drain cell" like the vtc5a lets you get the amps out quicker, but the number of amps that the cell discharges is determined by the flashlight. If your light only needs 3 mAh, that is all it will "take" from your cell. But in a case like this you are better off with a high capacity 3600 mAh cell than a high discharge cell like the vtc5a that only has a capacity of 2500mAh since your light will not use the high discharge rate of the vtc5a.
You will likely get better answers than mine from others on the forum, but I understand your confusion. I was where you are a year ago. I started with an "off the shelf" light and protected cells. It worked fine and I was happy with my light. As I read more I learned more and now pretty much all of my lights are modded by Vinh at SkyLumen and I use unprotected cells for the best performance in those lights. Keep reading and asking questions. People here are happy to help out. It is sometimes like drinking from a fire hose when you are just getting into all of this flashlight, battery, charger stuff, but it is a lot of fun too.