When the grantor of a grantor (living) trust dies, the trust becomes irrevocable. This means that any income earned by the trust after the date of death is reported by the trust on Form 1041. Likely the trust will need to obtain an employer identification number (EIN) but the grantor trust probably was using the grantor’s Social Security number.
A tax credit directly reduces tax liability, as opposed to a deduction that reduces income subject to tax.