Ohio Preparers - STRS & SS question

[Jack from Ohio]

We have a client that is a contracted teacher for a school system. Paid in 1099-Misc.

When we prepare her return, SE tax is calculated on the profit, which is 95% since she has little in the way of expenses to offset.

The School is withholding STRS from the amount they are paying her. The School claims that she MUST participate in STRS.

Here are my questions:

1. How can a contracted worker (non-employee) participate in the STRS?

2. If it is true that she must participate, (playing what-if here) can she participate in both STRS and SS?

3. If she cannot participate in both, but must participate in STRS, is there an exception for SE on her tax return?

4. If she cannot participate in STRS, is there a process to get those monies withheld refunded?

Additional information:

The School is getting a Title 1 grant to pay her. The School claims that they cannot hire her or the grant funds will dry up. (I have no idea how Title 1 grants work, so I am unsure about this)

Any ideas, or experience with this?

[Margaret CPA in OH]

Although I am in Ohio and actually did work as a sub teacher briefly, I have never heard of this situation.  I was paid as an employee.  You've probably already checked this but, if not: https://www.strsoh.org/  Surely someone there will be able to help you.