There is no law that requires them to deduct anything.  They decided not to keep a log.  Why pester them for facts now, when contemporary records don't exist and the Cohan rule doesn't apply to mileage?  Higher income might result in greater EIC, anyway. 

Having summarized the situation, I will suggest that my friend who occasionally does DoorDash tells me it works out to about a dollar a mile.  So, if the 1099 shows $10,000, ask them if 10,000 miles sounds about right. As to whether and how to check that box, let your conscience be your guide.