Can a car battery Solar maintainer damage battery?

A solar charger around 2.5V, plugged into my always-on cigarette lighter. Charging into my Optima red top battery in my 01 Ford Explorer. I do not drive my SUV for sometimes a week at a time and that can cause battery to get low(and I have to call AAA). -No battery drainage or alternator issues, just inactivity-

So I want to get this battery maintainer but I fear it might overcharge the battery if left on for for a week or two at a time. I do not know a lot about batteries so please let me know if my concerns are legitimate.

Thank you

Added (1). I'm probably going with a 5W panel. Will it overcharge the battery at all, even if left charging for an entire year?(hypothetically)?

I doubt the solar charger will put much into your battery if anything at all. Car batteries need about 14.5 volts input to benefit or at least 12 volts to maintain. 2.5 volts is so little it can't have much effect. But you can be sure it won't harm the battery.

If the solar charger doesn't put out 12 volts 2.5 amps it won't do a thing. A battery should be able to sit for a good month and still start the car. You have a problem with either the battery, alternator or a voltage draw. I'd get the charging system tested again. If you don't have 13.7 volts at the battery terminals with the motor at 1,200 rpm one of the diodes is bad and you will only be getting a surface charge. That's what your problem sounds like to me.

There are some such as battery tender that maintain the battery, as in shut off when your battery's fully charged, Run about $60 bucks, Or if you already have a standard solar charger you can buy just the controller for about $30, Without said controller, Yes you can boil out your battery, meaning destroy it.
But as your other poster stated, Your battery if in good condition and no parasitic draws should hold a charge almost indefinitely, Its not as though its charge just evaporates, so you have something amiss,
I've installed a few of the higher end Battery Minder solar chargers on some odd ball mobile equipment our county Office of Emergency Services has, and they have all kinds of crazy stuff that just sits around until a disaster pops up, In which case when you need it, it better work, But these are on things like equipment trailers and mobile morgues, If I had a vehicle battery going flat I'd get to the root of the problem and fix it rather than going the route you appear to want to go.
And just a heads up. If your going to VatoZone or somewhere like to have your battery and charging system checked, There's a reason these people work at an auto parts store

If the panel supplied 2.5V, the battery would FRY the panel, not the other way around.
That said, When the engine is running, the Alternator is CONSTANTLY supplying about 14 volts. If the batter can't handle a constant 12V from the panel, it is already beyond its useful life.

No worries, it will not overcharge or damage your battery. However, one week of inactivity is not long enough to need to call AAAfor a jump, so you probably do have a charging problem, or your battery is almost toast. One of the two. A month isn't even long enough to drain a battery.

If you hook a 2.5V 5W solar panel up to a 12V battery, it will probably burn up the solar charger or drain your battery. If you run the vehicle at least 15 minutes every three months, you don't need a battery charger if the battery and charging system is decent and you don't have to crank the engine for a prolonged time to start it.