Do I have to tell DTA I got a tax refund or Earned Income Tax Credit (EITC/EIC)?
No. Tax refunds and EITC do not count for DTA SNAP food benefits or DTA cash benefits. And, assets do not matter for any DTA benefits (except for in extremely rare SNAP cases for households with a member disqualified due to an IPV or elder/disabled households with income over 200% of the Federal Poverty Level).
You do not need to tell DTA about these payments.