Quick disclaimer, this method does not physically remove the outlines on the viewport frame, but it does make them near invisible.
The outline colour is directly related to the BackgroundColor3 of the viewportframe object, and setting this colour to a grey-ish colour seems to remove it.
What I do is just set the color to whatever is behind it. That usually makes the outline completely invisible. If there isn’t a background or there are many colors in it, I’ll try to find a color that generally matches the object in the viewport frame.
Thats why I chose grey in this example. Its a fairly neutral colour that blends in with quite a lot of backgrounds. But I do agree that it could be changed based on your background!