You're very welcome!
Your rear axle carrier looks pretty dirty inside.. I'd use the service manual to help you tear it down, then clean all the parts & hardware in solvent to ready for inspection & reassembly. By then you'll know what you need to replace and can order those new parts.
You can use Partzilla as a reference for parts & part numbers plus an interchange list appears on each part number page. You may wish to buy your parts elsewhere though. Partzilla is slow and unreliable.
2003 TRX250EX A Honda ATV Parts
I recommend you avoid all china made parts (they're useless garbage) and buy OEM only, unless buying a high performance aftermarket part that is a legit niche product. Many (most nowadays) bearing suppliers are selling cheap chinese bearings, so play it safe and buy OEM unless you have a better reason not to...
If your carrier bearings are still good, pop the seals off from them for cleaning in solvent and a fresh repack of grease. Any new OEM bearings you may buy for replacement will require the seal be popped off one side for adding additional grease... the manufacturers are all shipping new bearings nearly empty of any grease nowadays... pack them with a knowing smile!
If you have any questions for us.... we're all ears...
Enjoy your work!