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For refinancing purposes, it does not matter. Any lender you approach for refinancing will likely have an underwriter or an inspector (or both) evaluate the worth of the property independent of any taxes or the amount that it sold for, and go off that amount primarily.
For tax purposes, this involves excise tax. Please find the chart for this HERE. Under WAC 458-61A-215, no excise tax applies to quitclaim deeds "given for the sole purpose of clearing title if no consideration passes otherwise. This rule does not apply to deeds executed for the purpose of adding persons to title, except in cases of persons added to title for co-signing security purposes only." Your matter may or may not fall under this. If it does not, the amount typically goes off the estimated value by the county if the deed is quit claim.
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