Yes, the MCC requires a trade-off according to Form 8396. Your $27,000 mortgage interest is required to be reduced by the amount mortgage interest credit. In your case,$2k. This changes your sch A mortgage interest to $25k. This has some effect on taxable income.
Example:
Pretend you are in the 22% tax bracket and lose $2,000 of deductions that means $440 less refund.
$2k credit added -440 lost from the increased income = $1560 increase in refund.
Depending on your tax bracket, the jump is more noticeable.