Recolour .eps file

The way the bounding box takes a whole rectangle instead of showing you the anchor point makes it look like an image (pixels) embedded into an .eps as @Ton Frederiks rightly observed. Meaning that most illustrator options will not work. You need to either locate a proper vector .eps file or digitize this one so it's not longer a raster image.

Looks like an image. 

You mist first convert it to vectors. You can use the Pen tool or try Image Trace