Again, it is your child’s grant, and your child is benefiting.
You have no obligation to pay anything for your child’s education, unless you agreed to it in the divorce. How you split costs is up to you or your divorce decree. If it says you will split costs evenly, I’d say those are costs after all grants and scholarship. If your child’s cost of attendance is $50k, and student gets $8k in pell grants and $10k in need based aid from the school (or other scholarship), I think you’d take $50k less $8k, less $10 for a final bill of $32k (to be split or covered by your child with loans or work). Remember there is also an ATOC tax benefit that can be allocated, and perhaps other tax benefits that may or may not have been assigned at divorce.
I get you are arguing that the Pell grant should be in your contribution because your tax info secured the award, but it is your child’s award not yours.