What can I do about these exposed grounding rods?
Never assume a rod that is not being is not needed!
If the #6 copper has been ripped out it probably needs to be replaced.
The short one is easy dig around it and drive it below the sod.
Next dig a trench to the other one and I would use a piece of metal pipe to straighten it out and drive it below the sod.
Using the acorn nut on the rod connect #6 or larger copper wire rod to rod to your service panel. I have worked on a few homes that for some reason the ground was removed (this can be hazardous to your health)
So unless you can verify you do have a solid ground drive them a bit further. If new rods were driven they can be pulled up or cut off.