@ dude: Das trifft es nicht. Es ist eher was im Sinne von "glad to see you gone".

that's exactly what this saying means: go now and don't let the door hit your tired ass as you're leaving

@ dude: ach so! Danke für die Hilfe, das kannte ich noch nicht.

possibly also

don't let anyone stop you...

not nice

I agree with dude and noli

@Fragende: "dass wenn jemand denkt, woanders geht es besser"
Speaking directly to the person one could say: "you seem to think the grass is greener on the other side of the fence"

a bit more friendly

And I still treasure an LP from the 'New Christy Minstrels', featuring (amongst other songs) the title:

'Green green, as green they say, on the far side of the hill. -
Green green, I'm going away, to where the grass is greener still.' . . .

More or less the same as "don't let the door hit you on your way out." I just think the sting comes across a little bit better when it's shorter and sweeter.