Here is a thread that I discuss this problem when importing a Filled SVG into Blender.
In a nutshell, a filled SVG has vertices for the Curves as well as for the Filled Faces…which float on top or underneath the curve vertices that is why you see that real mess on the import…
Far better to import as just a curve, with-out the fill…but in your case, this is not really possible as it is an image file… the best solution I can think of is somewhat @Fowl was saying is to use clean up and remove doubles…but that will take care of only some of the problem…better to delete the faces > cleanup and remove Loose…select the curve and convert to Mesh…then re-“F” ill the faces and texture with the original colors…a lot of work but would get better results in the long run.