By example:

Is there a tool or a way to fill the white X shape so that the colors and patterns around it will blend into it as automatically as possible?

I.e., I want to remove the X as close to the picture as possible.

I'm working with GIMP, but I welcome answers in any software.

I know of the clone tool, but it's tedius. A pattern isn't good, since it needs to be adjusted by the colors and shades of the nearby pixels.