@Kaztek, for example with this source, you should crop it first before putting it through remove.bg so that the face quality remains as high as in the original source.

Here's what I mean: a couple of videos on how to use remove.bg, one when combined with Photoshop and another using photopea.com, which is a free online app so close to Photoshop that it has the same shortcuts, layout and icons 😉 If you don't have Photoshop, photopea.com is the tool I would recommend to use to tweak the draft cut produced by remove.bg. It's more powerful and versatile than GIMP and other similar tools.