Can post-processing remove mesh netting artifacts when shooting ice skating through a rink barrier?

Sometimes, but only partially. If the image is focused on the skaters and the net appears as a repeating pattern, frequency-based tools such as a Fast Fourier Transform workflow in Photoshop or GIMP can reduce periodic interference. This tends to work best when the mesh pattern is fairly regular; uneven areas may need to be treated in sections, and manual retouching is often still required. Don’t expect a perfect restoration.

If you can return to the same position, another option is to make a matching frame without the skaters, align it as a second layer, and use blending/masking to subtract or replace the netting. This can be effective but is fiddly and depends on near-identical framing.

Shots where autofocus locked onto the net, or where the mesh is strongly visible and blurred across the subject, usually can’t be truly saved.

To reduce the problem at capture, get as close to the net as possible so it falls far outside the depth of field and becomes less visible. That won’t always eliminate it, but it can help a lot.