https://ttlc.intuit.com/questions/2903043-how-do-i-delete-a-k-1

That answer should be prefaced by indicating if the existence of a K-1 was erroneously indicated, you may need to delete the underlying forms.

First, how to get off that page.  When you're in the state tax return, click on Show Topics near the top border.  Scroll down to a desired topic and click on it.  

Second, why state TT is asking you for K-1 info.  If you entered K-1 info in the Federal, then some states will automatically present you with K-1 questions.  With some partnerships, there is state-specific K-1 info.  It may indicate the state K-1 numbers, or the adjustments that should be made to the partnership income.that flows from the Federal.  Unfortunately, TT States do not ask for K-1 info in a reasonably uniform way <argh>, so adding supplemental info notes can be useful.  

If the partnership provided no state-specific numbers or adjustments for the states you file in, then the K-1 numbers are the same as for the Federal and 0 adjustments are needed.  But you'll have to go through the state K-1 questions, nevertheless.

Not all K-1 forms arise from a partnership.

True that K-1s can be received for estates, trusts, and other entities, but there still could be state-specific info on them.