So you import the glTF model normally (such as saving it in your Godot project directory). Then, do not drag the glTF onto the scene. Double-click it on the bottom left (where your project files are) and a popup window appears. Choose "open new inherited". Then in this new scene, you can save the scene (with some name, this will be a tscn file). Then you drag the tscn file onto the scene and only edit that (not the original glTF file).
If you are dealing with lots of textures and need special options (such as disabling filtering or mipmaps) then you should adjust the default import options before adding the glTF files. Just import one texture (could be anything, just to test it), set the options you want in the "Import" tab, then click "Preset", and choose "set as default for texture". Then any additional textures you import will get the same settings.