I have a K2 on my site and only registered users can post comments through my moderation.
So if some user posts a comment and fill up field e-mail with the e-mail existing in system, this comment cannot be accepted by k2 system and k2 say, that user with this e-mail already existed.
How I can turn off such e-mail checking?

You cannot. If the user has an account with this email he needs to login. Otherwise anyone can pretend to be some of the site administrators if they know their email.