Hardship withdrawals are
not eligible for rollover; the money cannot be put back into any retirement account as a rollover contribution. A hardship distribution is subject to tax and is subject to an early-distribution penalty unless a penalty exception applies:
https://www.irs.gov/retirement-plans/plan-participant-employee/retirement-topics-tax-on-early-distri...Even if you had purchased a home with the money, you would still have been subject to the same tax and penalty.
