normally the custodial parent claims the child. The custodial parent can allow the non-custodial parent (NCP) to claim the child but must furnish them with a signed form 8332 which the NCP must include with their filed return
if you delete the child and are the custodial parent, you will lose out on many tax benefits
such as Head of Household filing status and certain credits.
if you are entitled to claim the child and did not consent to the ex claiming them (by supplying form 8332) claim the child and file by mail.
The IRS position is that the custodial parent is the only one entitled to claim their child despite what the courts may say or what's in the divorce or separation decree UNLESS you give the NCP that form