No. No you may not.
https://cssd.dc.gov/page/temporary-assistance-needy-families
As a parent you should be supporting your child(ren).
Why shouldn't you be reimbursing the government for some of the money going to your child(ren) in the form of TANF benefits?
The only way you can get the support order "cancelled" is by
either:
1) The custodial parent getting totally off of TANF benefits, AND the custodial parent agreeing to a downward child support modification.
OR
2) The child(ren) ceasing to qualify for child support, either due to emancipation, adoption, or death - whichever happens first.