Hi Playful Panther,
There is nothing specific in the Laws of the Game regarding this. If it were to be mentioned specifically, i would imagine it would be included in Law 16: The Goal Kick. But it is not, so we therefore have to infer the answer from the rest of the laws.
In my opinion the answer lies in Law 4: The Player's Equipment. Here it states: A player may use equipment other than the basic equipment (footwear, shinguards, socks, jerseys with sleeves and shorts) provided that its sole purpose is to protect him physically and it poses no danger to him or any other player.
This law allows people to wear, for example, a knee strapping for their protection, but prohibits them from using extra equipment for example jewellery.
So, the way i would deal with this is the same way i would deal with a player wearing jewellery. Warn him first that it is not allowed & he must correct his equipment. If he continues to use it, i would caution him for Unsporting Behaviour.
I can't imagine any kind of injury a GK would have that would be protected by using a tee... In my opinion, it is an unfair advantage over the other GK & usually, if they are injured they just let a team-mate take their Goal Kicks.
I would be interested to hear the other referee's opinions on this. Since it is not dealt with specifically in the Laws, there may be some differing opinions on it & open discussion is the best way to ensure some consistency. But the above is how i would deal with it in one of my matches.
Hope this helps,
Girl in Black!