My mother passed away in Sept 2017. Since then she received a check from renters rebate for $450. Do I need to go thru probate for a small amount check?

She had no assets, no savings and I finished paying off her funeral and bills with a $10,000 policy she had. I was the beneficiary, and POA. Since then she received a check from renters rebate for $450. Do I need to go thru probate for a small amount check as that is all she has in her estate? The check is made out in her name, not to the "Estate of", and I closed the joint checking account we had.