I also have a 2001 TC25D. For a long time, there was no corrosion or "cottage cheese." Then three weeks ago, after having let the tractor sit for a month or so (dry here - not much to mow) I went to do the last mow of the year. The tractor turned over slowly, then started. Halfway through the job, I turned it off, dismounted and let my bride take her turn. She turned the key and there was nothing but the clicking of a starter not getting enough juice to go. I opened the hood, and there is was. Enough cottage cheese on the positive terminal to fill a week's worth of diet plates at the local diner. The negative terminal was about half that bad. Worse, it was clear that there had been a fair amount of spattering and leaking that I hadn't noticed earlier - the bracket and plate were full of rust and there were the beginnings and then some of corrosion on the radiator, some of the hydraulic fittings, and the top of the tie rod joint, both on the positive side.
I pulled the battery (the clamp screw on the positive terminal was so corroded it snapped like a pretzel) and scrubbed everything I could reach with a pasty mixture of water and baking soda. Man, did that baby foam up! I then ordered an Optima Yellow Top from 1st Optima Batteries (Shown on the Optima site as a vendor) for $139 shipping included. Steep? You bet. Cost of replacing radiator and other corroded items steeper? You bet. I'm still under warranty, so the only hurt is the cost of transport to and from the dealer. In a few months the warranty will expire. Using an OEM battery will eventually lead to similar problems. That would then be my bill to pay and rightly so. I think of it as a potential "stupid" tax - similar to the $55 towing bill I paid when I got the tractor stuck in the mud while it was still new.
FYI, Optima now has a 51R, with positive on the right. It fits the 25D perfectly, and it packs a great punch. Like the mechanic in the old Fram oil filter commercials used to say, "You can pay me now or you can pay me later."
Good luck!