How to tightly fit an image into a different image's frame using Gimp

I'm new to GIMP and photo editing, and I took a more complicated approach than Billy Kerr's answer. In GIMP I clipped out the screen from the original phone. The portion that was clipped out was transparent. I then placed the image I wanted in the transparent area, in a layer below the main image.

This is more work than Billy's answer, but I believe it will yield cleaner results. Personally I had issues in accurately painting in the layer mask.

You can use a layer mask to achieve an edit like that.

1. Paste the screen shot and then transform (Shift+T). Make sure none of the Constrain or Pivot options are checked in the tool options, so that you can freely distort the screen shot to fit the phone

2. Click and drag the corner handles to fit the phone screen. Note: the Image Opacity slider in the tool options can help you get it right, allowing you to see through the layer as you transform it.

3. Add a layer mask to the screen shot layer, filled White Full Opacity

4. Make sure the layer mask is selected in the layers panel, then with the Paintbrush tool, paint in black on the layer mask to reveal where the finger is on the layer below. Note: if you make a mistake, you can paint over it in white.

Example: