We received a refund on our funding fee from our mortgage lender. The amount is $10,500. How much taxes should we expect to pay?

if you deducted the funding fee in the prior year, it would be taxable to the lesser of the $10,500 or the amount your itemized deductions exceed your standard deduction for that year.

if the refund was received in the same year paid, it would just reduce the deductible amount.

we can't say how much taxes you'll pay if different years are involved because we know nothing about what your taxable income before the refund will be.  

here are the 2019 tax tables that you can use to judge

$0 to $18,650 10% of taxable income
$18,650 to $75,900 $1,865 plus 15% of the excess over $18,650
$75,900 to $153,100 $10,452.50 plus 25% of the excess over $75,900
$153,100 to $233,350 $29,752.50 plus 28% of the excess over $153,100
$233,350 to $416,700 $52,222.50 plus 33% of the excess over $233,350
$416,700 to $470,700 $112,728 plus 35% of the excess over $416,700
$470,700+ $131,628 plus 39.6% of the excess over $470,700