If the reporter cashed the check for the month of death (and any later months), do not ask for a refund. Advise the reporter that the Treasury Department (TD) may request the funds back from the bank that cashed the check for a period of up to 12 months from the month that SSA learns of the death.
For example, if 5% of your non-Roth IRA are non-deductible contributions, then 5% of the conversion amount must be non-deductible contributions, and the rest must come from the deductible contributions, including earnings and rollover contributions.
When you got a distribution check from the IRA, then reinvested it in your 401k, you executed an indirect rollover. Rollovers from an IRA to a 401k are allowed by the IRS if the plan permits it. If you rolled the money into your 401k within 60 days, the amount should be tax-deductible.