Those squares are showing you the effect of the alpha channel. The alpha channel is what controls how 'shiny' cars are in game.
White alpha channel = Shiny | Black alpha channel = Dull | Every value of Grey is something in-between
In GIMP, where the alpha channel is Black, you see no colour, only the checker background.
Where the alpha channel is White, you see only colour, no checker background.
Where the alpha channel is a value of grey, you see something in-between.
When you edit the texture, you probably keep the existing alpha channel, or you'll have to make a new one at the end (or have very shiny cars).
To do this:
1) Right click on your layer in this toolbox on the right and click 'Add Layer Mask':
2) Select 'Transfer Layers ALhpa Channel'
3) Select 'Disable Layer Mask' (to hide the alpha channel's effect) and Unselect 'Edit Layer Mask' (otherwise you'll edit the Alpha Channel instead of the texture itself)
After you've made your changes, right click again, un-check 'Disable Layer Mask', and then 'Apply Layer Mask'.
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