I feel like the original implication was that you couldn't close your third eye at all, or you end up like Koishi. Otherwise if she could temporarily close her third eye (and visibly indicate that she's not reading minds) it seems like there'd be less reason for her to have been hated in the past. But I guess there was nothing set in stone about that.
I'm pretty sure she didn't
close the eye, she just shook off Seiga's hand and moved it away so it would no longer point at Seiga. The eye is visible in one more panel a few pages later, when Satori looks out the window, and it's open as normal, its pupil is just covered by the window framework.
It seems that Satori can focus her eye on a specific person to help her read that person's mind with more precision, and that's what Seiga objected to. She either doesn't know about the full implications behind a satori closing her third eye, or she DOES know, and her request is carrying the very thinly veiled threat of "close that eye (for me, metaphorically, by looking away), or I will close it for you (for everyone and yourself, literally, by doing to it whatever Koishi did to hers)".
As an aside: Satori personally doesn't care if she's being hated for reading other people's minds. Her stance is that reading minds is awesome and haters can be haters all they want.