Searches for dipole form of anisotropies (on luminosity distances) in the universe with type Ia supernovae
Isn't the point of using type Ia supernovae that they have an estimated distance that is independent of redshift?

${\bf \hat{n}}$ here is not the direction of the CMB dipole, it is a free parameter in their model.

If distances were being estimated using redshift I guess you would have a point.