This is a bit speculative because I've not tried this directly in Mage but the question appears to include the option of a 3rd party Mage who is attempting to alleviate a friend's blood bond there could be some use from lower level Mind effects.
Mind 2 can be used to influence emotions which would provide a way to make it easier for a thrall to resist the blood bond by dampening their feelings towards the regnant. e.g. Lowering the difficulty of the willpower roll by the number of successes on an Arete roll. If an extended roll was allowed then the Mage could make this last quite a long time.
Mind 3 can be used to influence the another person's thoughts which could be used to encourage thoughts of rebellion in the thrall. This would inspire the thrall to attempt to resist the regnant more often and also lower the difficulty of the Willpower roll as per the Mind 2 effect above.
Mind 4 could be used control the mind of the thrall and force them to resist the blood bond (by making the usual Willpower rolls as above) but I suspect this would actually be counterproductive compared to the more subtle approach of Mind 2 or 3
The Mage friend could use a Mind 2, 3, or more effect on the regnant to promote better behaviour towards the thrall. Obviously this would need to be done very subtly to avoid recrimination.
Note that Mind effects used against a ghoul or vampire use the target's Willpower+3 as the target number making the successful use of these effects rather difficult.