Same thing... my first character was a GOO Warlock and playing for a few hours, I realized that my primary ability... didn't seem to ever come into play.
So I was thinking about it and there are things that they could do.
1) Since your telepathy allows you to communicate non-verbally, you'd be an ideal scout when the party is sneaking. You could warn people where the bad guys are and if it was safe to move, etc.
Gameplay effect: anyone within telepathy range (30' iirc) of the player gets advantage on stealth checks.
2) Similarly, you could say that through practice, you've managed to hone the skill of implanting suggestions into people's minds while talking to them.
Gameplay effect: GOOlock gets advantage on Persuasion and Deception checks.
3) Since you can communicate with minds, you could argue that this also allows you to detect a mind.
Gameplay effect: give GOOlock the ability to detect invisible
All of these fit thematically and would be useful. If Larian were to implement all of them, they'd probaby want to put once/short rest on them. (Works for 2 and 3, but not so much for 1.)
I think there are lots of ways that you could implement something that would have an actual gameplay effect/advantage while still being true to the intent of the class ability.
Oh, and (4) the easy way out is to just grant the player a choice of 1 or more of the following bonus cantrips as a "trick of the mind"/implant suggestion kind of thing:
Friends, Minor Illusion and/or Thaumaturgy
Not quite the same as telepathy, but it would fit and it would make GOO warlocks far less useless than they are right now.