First, don’t condemn the battery until you have it load tested. Generally, older batteries aren’t going to have the “poop” a new one does, but that doesn’t mean it needs to be replaced on a calendar date. If it comes up bad on a load test, then replace. If it comes back good, re-install. If it comes back “weak” but good, then you can make the discretionary decision to replace or not.
Also, not all battery tenders are created equal. Some only have a “trickle charge” setting. Meaning: its only going to charge at somewhere between .5 to 2 amps, but it always is on. “Smarter” ones have multiple charge modes and once the battery is up to charge, they switch to “float” mode. Meaning it essentially shuts itself off and just tops the battery up as it senses a drop. Its more complicated than that, but thats it in laymans terms.
Older “tenders” tend to be the trickle charge type, newer ones are the multiple modes type. Newer ones incorporate the monitoring circuitry and the mode controls, where the older ones are pretty much just a ac to Dc converter.
The older types were sold as “battery tenders”, but they really weren’t. They were intended to slow charge the battery and be removed by the user when the battery was full. Then, the user would have to go out and charge the battery every month or so. The new generation, as I mentioned, monitor themselves and switch to the most appropriate mode based on what it senses from the battery. Hence, current battery tenders can be left on the battery for the entire storage period, regardless of how long it is. But you still need to read the specs and instructions to know if it can be plugged in and forgotten about until spring.
Even a trickle charger (older type) can boil a battery dry, if left on long enough.
For the battery tray:baking soda and water to neutralize any acid and paint fixes up any damages.