Editing PNG in GIMP: is it possible to remove lines (used as arrows) and extrapolate the now blank squares?

I'm using GIMP to prepare this PNG file for vectorization in Inkscape. I've noticed that the vectorization process makes removing these lines far more tedious after the vectorization than before. Removing these lines by using the "Select by Color" tool leaves transparent pixels and I'd like to know how I can give these pixels the colour one could expect them to have based on the colours of neighbouring squares. Is there any way to systemically extrapolate these colours?

This is the PNG I'm editing.