No, I don't think you have a right to be upset. It is not your horse. You pay for the right to ride it, that's it. She can clip him, dye him, shoe him, designate what tack may or may not be used on him, say whether he can jump or not, etc. You can either go along with it, or end the lease.
In fact, if it were my horse, and I heard that the leasee was complaining that I pulled his mane, I would not be inclined to renew the lease to them.
The only way for you to have full say in what happens with a horse is if You own it.