*joining in late so bear with me if I get too redundant*
um.....nope. Don't fan this flame.
I agree that you should not do this, just for the sake of harmonics. Don't rock the boat.
But there was something in the OP that really made this less complicated. I have come to realize that someone viewing the situation from the outside (In this case) the wife can get a totally different perspective. Whereas the TG in this case thinks they have found a "friend" and pal, the woman sees other signs. And trust me those signs are often missed by the person whom the signs are meant for. I have noticed this myself. When someone does something (like playing with their hair, playing coy, dangling a shoe) the person they are aiming at (OK I'll say it the hetero often clueless male) doesn't see it. Even when they are told by the outside person they deny it. Then weeks or months later it becomes blatantly apparent. In the meantime the blithely clueless target is now knee deep in swamp water. This may not be cut and dried as all that because we know the GG has her alert set on high and may be misreading as much as the target, but she saw something. Set her "spidey senses" tingling. I would not ignore this. At least I would beware of the fact that the GG has some worries. And it is easier to avoid the potential than it is to try and repair the damage.
I don't like the jealousy game. I personally try to not be jealous of whoever I am with a the time. They are their own person as am I. I have friends of both sexes and both sexual preferences. I can and do maintain these relationships without getting any deeper than just friendship. So I know it can happen and this whole scenario could be over dramatized. Could be, but still there had to be something there the GG saw. I say cool it, if it is to be, it will be. True friends don't "punish you" and true friends don't mind taking it slow and they understand that there may be issues that have to be addressed. If this GG really just wants to be friends they will work slowly to gain the GG's trust and friendship as well as the TG's. There are people out there who get a thrill driving a wedge in a relationship and when they accomplish that they are gone. That is another worry I have with the OP. It's a game, and the TG and GG are just pawns.
Long answer to a short question but nope, no way, uh uh, wouldn't do it, wouldn't be prudent.
(PS I hope this was all hypothetical and just a bad dream )