Given a SHA-256 message block, is it possible to undo the transformation of the internal state?
No, this 'unappend' operation is effectively infeasible for the SHA-256 hash compression operation; there is no known way that is less expensive than brute force.

Such an 'unappend' operation would reduce the time taken to generate preimages from $2^{256}$ to $2^{129}$ hash compression operations (assuming that the unappend operation is as cheap as the forward hash compression operation).  This would be done via a meet-in-the-middle attack, where in the most straight-forward implementation, you generate one list of $2^{128}$ intermediate states (from $2^{128}$ prefixes), and you generate a second list of $2^{128}$ intermediate states (from $2^{128}$ postfixes; starting from the target hash, you use the unappend operation), and search for a common value in the two lists.