My trainer has a sliding scale of bonuses for the groom based on finishing position.
I send a $ 20 bill and ask that he/she give it to the driver on their next meeting. The only reason I do this is that the driver should remember when the horse wins, there will be a few extra bucks in it and the driver might drive your horse if they think they have a chance to win.
If I am watching my horse race and they win, I give them the 20 myself. A great way to meet your driver after a win and they are very surprised. I went to watch my horse in late June at the Meadowlands and the horse won in a 3-way battle to the wire. I was still in the paddock and tipped Todd McCarthy personally. He was surprised by this, but took a couple of minutes of his time chatted with me between races.
In theory, the trainer should bill the owners for this additional expenditure/