If your final results need to be vector paths, then GIMP would not be helpful. GIMP is a raster editor. I'm not sure which message you might have seen (I've been around this community for over 10 years!). I do recall a couple of times recommending GIMP for people who want to warp a photo around a sphere. I think GIMP has a tool to do that.
It should be relatively easy to trim off those edges using clipping. However, the pillow object has also been traced, which means that it's not a single path. Instead, it's made of 2 paths - inner and outer, sort of. So you'll need to prepare a proper clipping path.
-- Select the pillow path
-- Duplicate (Edit menu or this button
)
-- Path menu > Break Apart (everything is going to go black when you do that, but don't worry)
-- don't deselect anything
The next steps are optional, but they might help you to see what you're doing, while you're learning. Once you've done it a few times, you could skip these steps:
-- Object menu > Fill and Stroke > Stroke Paint tab, click the solid colored, square, blue button
(this adds a stroke, or outline, although you probably can't see them yet)
-- Choose some wild bright color for the new strokes. It will help you to see them easily, on top of the black pillow outline.
-- Object menu > Fill and Stroke > Fill tab, click the big X button
(this removes the fill)
So now you can easily see the paths. My guess is that you'll want to use the inner path for clipping. If you use the outer path, then the fabric is going to look like it's on top of the pillow outline. Using the inner path will make it look like the fabric stops at the pillow outline. But you can experiment with them to find out which one works best.
Whichever path you decide to use, select it and the fabric object at the same time. (If you haven't already learned, holding the Shift key will let you select both objects at the same time.) Then just do Object menu > Clip > Set
Don't forget to delete the other path.
Let us know how it goes