Is it permissible to perform Umrah while a blood expiation (kaffarat dam) has not yet been fulfilled?

If a pilgrim is obligated to offer a sacrifice (dam) during their first 'umrah due to missing an obligation, they are permitted to perform a second 'umrah before offering the sacrifice, as long as they have exited the state of ihram from the first 'umrah. However, if the sacrifice is obligatory due to a sin, then, according to some jurists, it becomes immediately obligatory, and thus, delaying it is not permissible.