That is a GE panel. See all those small holes in the back? They are designed to mount different length ground bars and other things.
Go to Home Depot or Lowes, and find a nice long GE ground bar on the accessories rack they have above the circuit breakers. Mount the bar using the holes, probably on the right side. Move the green ground wire over to it. Remove the green screw and the offset/joggled bonding strap it holds down, and throw it in the junk box. When done, move your green ground wire over to the ground bar.
Get two 8 ft ground rods while you are at the big box store and two approved connectors for them and enough #6 solid copper bare, to run from your ground bar to one ground rod and then to the other, without cutting or interrupting the bare copper wire, it must be continuous, and uncut. You can use smaller than #6 but you will have to protect it with conduit or other protection, while #6, being overkill, is allowed to be exposed, If I recall correctly.
Get a sheet of plywood and stand it up against the outside of the building where you are going to install the ground rods next to the foundation, and take a large sledge hammer and drive them in one at a time. The plywood is to protect the building's exterior while you drive the rod. It will go easy for a while and then get hard to drive, depending on the soil. Might want to slip the approved connector clamps over the rod before you start and wrap them in tape to make them stay put (tightening the set screw probably won't hold with all the pounding) as the rod will mushroom and the clamp won't go over it after you drive it in.
Charles