Is this ground attached to the wrong water pipe?
Grounding, bonding, water pipes, and your situation

The old-school way of grounding a house to the cold water pipe performed two functions, not just one:


It grounded the house electrical system to protect it against induced lightning and static charges
And it bonded the house plumbing to the electrical system to allow fuses to blow or breakers to trip if a wire faulted to the plumbing


Nowadays, Code requires us put in a dedicated electrode (ground rods or an Ufer for most folks) to deal with problem 1, and that's what you can do here -- running 6AWG copper from the main panel (optionally through a conduit) to a pair of ground rods spaced 8' apart and driven 8' into the ground will get you a serviceable grounding electrode in most areas.

You will still need to move the existing grounding/bonding wire from the hot pipe to the cold pipe and add a 6AWG jumper from the cold pipe to the hot pipe, though -- this will ensure that your piping is properly bonded to the electrical system so that you don't wind up with a shocking tub spout because the dishwasher shorted out.