Is it valid to work with the real and imaginary parts separately? Possibly, though you know the data better than we do. What causes an outlier? If there is a problem with the real component of a number, why would it not have impacted the imaginary part too?
I would assume you can simply work with the real and imaginary parts separately. But you cannot just REMOVE an outlier. You need to correct it. So you might decide to apply the tool filloutliers to each column of the arrray, separately to the real and complex parts, treating them as simply independent signals. That may not be totally valid of course. But can you do it? Of course.
You would use a loop over the columns of your matrix. Something like:
R = filloutliers(real(M(:,ind)),'gesd');
I = filloutliers(imag(M(:,ind)),'gesd');
You would need to play around to find what works best on your data of course.