Gravity doesn't attract, it is just the effect of time/space distortion. It is the movement of the pulsars (or whatever they are) which is distorting space/time and the waves created are radiating out from them. The waves couldn't be moving towards the pulsars unless they were created by an external source, which they clearly aren't in this example.
So Issac had nice hair as did Einstein- when you think about it Brian Cox has lovely skin. Maybe something’s going on. Aliens?
Having briefly read a bit on this, I don't think pulsars are the source of gravitational waves as they are quite small, but they serve to provide a means of detection. Pulsars do radiate electromagnetic waves outwards, but this isn't gravity. Gravity has all the appearances of an attractive force, but as you say Einstein viewed it as a distortion of space/time.
Sorry, I'm not talking about electromagnetic waves. Perhaps I should have said neutron stars instead of pulsars. The system in question is two pulsars rotating around their common centre of gravity. It's the to and fro movement of the stars relative to us which produces the reciprocating distortion of space to produce the gravitational waves. It's worth looking it up on Wikipedia: Two-dimensional representation of gravitational waves generated by two neutron stars orbiting each other.