To add on to this topic, I would strongly consider using these same methods mentioned in the OP for MeshParts. Consider this example:
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For Photoshop users:
Don’t download any plugins, photoshop has it built-in.
Layer > Matting > Defringe.
I usually enter betweeen 2-10 pixels to be safe, doesn’t really matter most of the times.
Black outlines? Vanished!
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This is going to help so many new UI designers out there! Amazing tutorial, Quenty! 
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I’d still recommend the original solution, because after trying that for a few minutes:
- The bleeding can clobber the color of visible pixels.
- The edges can get “chipped”.
- Sometimes it flat doesn’t work – note that in the first image, the outermost edges of the corner bits pretty much did not bleed outwards at all.
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True! Forgot to mention that it doesn’t handle stuff with opacity very well. The most common example would be drop shadows or any type of glow.
I’ve never noticed a major change around thin strokes though. Thanks! 
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Very sorry for the bump, but the GIMP solution isn’t working for this one image.
After importing it into GIMP, resizing the canvas and then doing the fix, I get this result.
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Idk if Roblox is screwing with my head, but this was literally workong for me this morning. Now, a few hours later I go back into my game, and all the images have the black outlines again.
I think you need to make sure you use the pixel size that fits the game
When you upload an image to Roblox and stick it in your game you sometimes see a black or white outline around your image when it scales. This is due to bilinear interpolation. This has been an issue on Roblox for a long time.
Here is a whole tutorial on how to fix it:
