Your 04 GTX is very similar to my 06 RXT....
I presume you took the intake grate off of the pump? That forward bolt hole goes all the way into the inside of the hull (there is supposed to be a blob of silicone covering it on the inside of the hull, but it frequently comes loose and then there's the bolt just sticking up inside there). Be certain when you put the intake grate back in that you use some Blue Loctite on all your grate bolts, and doesn't hurt to put a little silicone between the grate mounts and the hull to keep water from getting in there. if you don't use loctite and the forward bolt ever comes loose and falls out, there goes your grate it will break off and then water will start filling the hull slowly... you may not notice it at first, but leave it tied up at a dock to go inside for lunch at a marina and you may come back to a sunk SeaDoo!
I'm not sure but it looks like your engine may not be aligned properly to the jet pump, based on the way your drive shaft looks to be not centered in the hull pass-thru hole. That requires a special tool I believe. I've never had to re-align my engine though.
Your GTX has clearly been ridden in salt water and the drive shaft was not properly cared for at the end of the day (owner's manual details how to properly care for the GTX if used in Saltwater). That shaft is toast, get a good used one for your model off Ebay or buy a new one.
You might as well pull the pump off the back of the hull and examine the impeller and wear ring while you have it off. Check for any slop in the impeller bearings as well. Gap between impeller blades and wear ring should be about the thickness of a piece of paper.
To get the drive shaft out (once the pump has been pulled out), you have to pull back on the rubber bellows and stainless steel ring to expose a clip that's on the shaft (it prevents the shaft from moving backwards and keeps the SS ring from moving forward... the clip is sorta of hidden under the front of the ring) and then while holding the rubber bellows back use a large flat head screwdriver (or something similar) to push the clip off the shaft. It isn't easy to do without the proper tools but it can be done!
Once the shaft is out you can easily unscrew the clamps that hold the rubber bellows and carbon seal in place and take them out for replacement.
Then you put it all back together with fresh(er) parts... then align the engine correctly to the jet pump.
If you have a couple weekends to spare to work on it, you can do it all yourself with basic tools (and that SeaDoo engine alignment tool... I see used alignment tools for sale on CraigsList occasionally as once the engine is correctly aligned there won't be much need for the tool for a long long time again so most people put their's up for sale after using it).
Regards!
- Michael