I'm not sure what you mean when you say "Paid taxes related to a K-1." If you mean you had an interest in a business and entered income related to it on your personal tax return, so you paid taxes in with your other personal taxes on form 1040, you would have to look at such tax returns and calculate what those taxes would be.
How you intend to go about recovering them I don't know. Normally the way it works, is when you dispose of your interest in a venture, you will deduct your basis in the investment from your proceeds of sale, if any, and the difference is a gain or loss. If a loss, it is deducted as such on your current year tax return. If a gain, it gets reported as such on your current year tax return.
I don't know of any other way you can recover taxes previously paid.
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