I am not sure.
The only guess that I could make would be to suggest that at the end of Part 3, they buried him in sacred ground (if you will recall, they got Holy Water from a church, and sprayed it on the ground they ended up burrying him in at the end of Part 3).
The dog urinating on the ground would then have the effect of taking the sacredness (if that is even a word) away from the ground/soil.
I am not sure if this explanation was given in the movies. Or even if this explanation is correct.
This is simply my best guess though.
It may not have had any meaning however, and perhaps they just did it to try to be "funny".