Enter her information in the personal info section of TurboTax (TT) and follow the interview. Since she is under 17, she will qualify you for the (up to) $2000 Child Tax Credit and maybe the Earned Income Credit.
The child tax credit (CTC) is limited to your tax liability. The CTC is a non-refundable credit and can only reduce your income tax to 0, It can not help you beyond eliminating your tax liability. But, if you have more than $2500 of earned income, some or all of it is usually given back to you thru the "Additional Child tax credit". That is, part of the CTC may be on line 28 of form 1040 (2020 version) instead of line 19 (lines 18b and 13a in 2019). The ACTC is calculated on form 8812 and is basically 15% of your earned income over $2500. The ACTC is a maximum of $1400 per child (not $2000).
*A child closely related (great granddaughter counts) to a taxpayer can be a “Qualifying Child (QC)” dependent, regardless of the child's income, if:
- He is under age 19, or under 24 if a full time student for at least 5 months of the year, or is totally & permanently disabled
- He did not provide more than 1/2 his own support
- He lived with the relative (including temporary absences) for more than half the year
- He is younger than the relative (not applicable for a disabled child)
- If the child meets the rules to be a qualifying child of more than one person, you must be the person entitled to claim the child as a qualifying child (this essentially means that you have the parent’s permission to claim the child, if the child also lived with the parent more than half the year)
- If the parents of a child can claim the child as a qualifying child but no parent so claims the child, no one else can claim the child as a qualifying child unless that person's adjusted gross income (AGI) is higher than the highest AGI of any of the child's parents who can claim the child.
See full dependent rules at: https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Ret...
The child can be your dependent under either of two rules. Firstly, because she is a direct descendent of you (a child of your granddaughter) you could claim her if she lives in your home for more than six months even without a court order. Second, the court placement makes her a foster child which also gives you the ability to claim her as a dependent under the foster child rules.
How do I answer the question concerning relationship?
Either "foster child" or "grandchild" will be fine. (I believe Turbotax includes the option for grandchild, it is the same for tax purposes as great-grandchild.)