I can see the image you have selected is on a floating selection. That's probably the problem. Also by default, the Lock Alpha option is engaged on floating selections. You could deselect it, and that would allow you to use the eraser.
This shows the floating selection:
This shows the Lock Alpha Channel icon
When you paste something in GIMP, you then need to choose what to do with the floating selection. If you want to promote it to a layer of its own, right click the floating selection layer in the layers panel and choose "To new layer". If you want to merge it to the existing layer, hit the Anchor icon in the layers panel (or press CTRL+H). These actions will also release the Lock Alpha button.
You can avoid these extra steps when pasting if you click Paste As > New Layer instead. That will paste the image on a layer of its own, and the Lock Alpha option will not be engaged either.