Itachi takes this.
The Akatsuki were greatly affiliated with Iwagakure, having been hired by the Tsuchikage multiple times. There's no way the they weren't aware of the Jinton or how it works, especially since it was such a famous move, being the only Kekkei Tōta to be introduced at this time. It's apparent that Itachi is aware of how the Jutsu works.
That being said, every time Mū tries to pull of an attack on him, he can bring up the Susano'o which has the Yata Mirror, or simply counter attack with an even faster attack, the Amaterasu. Do note that while invisible, Mū can't attack at will, since his invisibility revolves around completely erasing the presence of the Chakra itself. Even if that wasn't the case, it'd be hard for a Sharingan user not to notice the flashing light which comes from the attack being formed.
Shortly put, Itachi has the ideal counter to Mū's strongest attack, the Jinton, along with having the Amaterasu on his side, something which would be hard for Mū to deal with. In the end, Itachi pulls this off.
