I have several old, paid mortgages still showing on my CR. When I added my new mortgage it produced a small bump, less than 20 points. But Credit Mix has three components - revolving, installment, and mortgage. All things being equal I believe having three bank cards, one installment and one mortgage active are optimum.
So you might see a small downward move in score, but should not do things that don't make sense financially just for credit scoring purposes. If your scores are in the 700s they'll probably still be in the 700s after you pay off the mortgage.
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