Eagle Board Editor: Garbage or stray marks of a particular component stays back even after moving it
Have you run a DRC recently? 

If there were errors shown by the DRC, they will remain as sort of cross-hatched lines when you move the object that caused the error.

Notice how in this screenshot I added a wire to create some intentional DRC errors, but even after I move the wire out of the way, the errors remain marked. Once you run DRC again they will go away. The same is true for components if for example there were Stop Mask errors, you can end up with lines around where the component used to be.

The solution as I say is to run the DRC check again after moving the object.