I received a refund from my 401k due to an audit of the 401k plan, can I put that refund into an ira to avoid paying taxes?

The excess distribution payment was due to "Nondiscrimination Actual Deferral Percentage Test Limits".  Does that change anything re: being able to put it into an IRA?  Could I simply put less into my 401K and put the difference into an IRA going forward?

Returns of excess contribution are explicitly prohibited from being rolled over to another retirement account.

Independently, if you are eligible to make a new regular deductible traditional IRA contribution, you can do so, but it has nothing to do with the returned contribution.

The excess distribution payment was due to "Nondiscrimination Actual Deferral Percentage Test Limits".  Does that change anything re: being able to put it into an IRA?  Could I simply put less into my 401K and put the difference into an IRA going forward?

That's what I assumed.  My answer does not change.  This is money that wasn't eligible to be in the plan because of the ADP test failure, so you are not allowed to treat it as if it was eligible to be in the plan.