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what is the amount of equity in the house

In other words, what is the difference between the price the house could have sold for at the time of the quitclaim and the amount of the mortgage

If it is below the exemption amount, it will typically not be at issue in the bankruptcy

however if it exceeds the exemption amount it would be considered a fraudulent conveyance and set aside by the trustee

A quitclaim or transfer of a debtor’s assets to a third party, for less than a reasonably equivalent value in exchange for such transfer, is considered to be a “fraudulent conveyance”.

Bankruptcy Code §548 provides for the avoidance of fraudulent transfers within two years before the bankruptcy filing date. Transfers to self settled trusts and similar devices are subject to a longer avoidance reach back (10 years).