Maybe Sage can block telepaths? Either that or Bashley likes her too much to check. I'm leaning more towards the latter since Sage was oddly friendly with the tumour.
I don't believe she'd be able to block telepaths because this isn't Marvel or DC.
The Boys universe isn't like Marvel and DC where there are endless different ways to get powers, way higher power ceilings, less limits on what powers someone can have, how long powers have been around, etc and with that comes a deeper exploration of the capabilities and limits of those powers, if that makes sense?
Like the reason you'd put the ability to block telepaths in a Marvel/DC story would be because there are so many examples of characters or even entire races who can use telepathy/mind reading, it would be bad writing in a lot of circumstances to not have the bad guys just go "we need to know something this person knows, grab one of the million telepaths and have them read persons mind".
So in order to not have that be the obvious go to every time, a writer will limit the in verse ability by making it so basically anybody can have anti-telepath protection.
This sorta thing doesn't work in the boys because the only way to get powers is V, the powers are usually pretty limited in scope, and they don't really come with protections past just being more durable.
So it's like, why would any supes ever need to develop defenses against something if there's never a logical narrative reason to do so.
The only reason sage would be able to block telepaths would be specifically because the writers needed her to in that moment.
Then there comes her being friendly to the tumor, and it's like, ok, that could make sense, but it's like why should be give them that?
Oh yea the tumor just decided not to say anything. sure. We shouldn't give these trash writers the benefit of the doubt.