Grammar Check anyone please?

years'

years’ - yes.

It's not teaching grammar I assume

The middle one as there's more than one year I'd say

I agree.
Or try:
I have been teaching for over seventeen years.
Or
I taught for over seventeen years.
Or
Having taught for over seventeen years.
There's always a way round a grammatical challenge.

Yep, 17 years'

I think the first one... not a contraction... not possession. I am a year 6 TA and teach a lot of grammar!

years'

First one

100% years'

Pop an “of” in to make it a straight plural:

Over 17 years of teaching experience

It is honestly years' OP. Don't listen to the others, who are wrong.

Totally agree, it needs an 'of' and no apostrophe.

Second one - the experience 'belongs' to the years.

Years'

Pop over to pedants' corner for confirmation it's years'.

I would say first one
Or I would put ‘17years of teaching’

Grammar book says it's 1.

Agree years’

It is absolutely years’. I’m a professional editor.

years' - because what it's really saying is "17 years of teaching experience". The implied "of" makes it a possessive, so you need the apostrophe. If the sentence were "I have been teaching for 17 years", there is no possessive, and therefore no apostrophe would be needed.

That grammar book clearly says it is 2 - years’ - in both the examples.