Are really up to the challenge of removing, disassembling to replace the oil filter, reassembling, waiting 24 hrs before replacing the oil, and then reinstalling the unit? Also it requires a super clean area and unit must also be super clean.
That Hydro Gear transaxle has a separate hydraulic unit and differential. As stated above changing the hydraulic oil would be a major chore. The gear oil would be some easier, (real easy with a drain plug). But sometimes it's tough to get it resealed without leaks. I'd leave it alone.
Edit: Looks like I was wrong on that hydro, the hydraulic unit and the differential is a combined unit. Would be worthwhile to change that oil I suspect. Did find this with a search:
"I wasn't able to find a drain plug as such, but there is an externally mounted gerotor pump on the bottom of the trani. Removing the pump allows all the fluid to drain out. I refilled with Amsoil synthetic oil and it's been working great."
If the drained oil looks good I'd not worry too much about the internal filter.
If you do remove the Georotor pump cover be sure to note it orientation as it is directional. Draining oil by this method will be slow if is anything like the last Hydro Georotor pump cover I remove on a Toro ZTR. I only lost a half pint of oil during the time it took to replace the o-ring which you remove the pump cover also needs replacing or you will have oil leakage afterwards.