How do they know the non-uniformities seen on the disk of π¹ Gru are real and not artifacts?
The paragraph you quote continues...


  The images from SQUEEZE and MiRa have very similar characteristics and are shown in Fig. 1 (see also the Image Reconstruction section in Methods)


In that section various tests are described including the reconstruction of simulated data, with similar interferometric coverage and signal to noise, from spotted and spotless (uniform) stars with limb darkening.