A 24V power supply will not charge it!
Charging a 24v lead acid battery requires 27.6v to 29.4v.
The ideal charging procedure is a constant voltage- generally on the high side of that range- until the current drops below a given threshold. Then the charger goes into a "topping" charge of perhaps the last 30% of the capacity, usually this is done in constant current mode. Then the charger should go into float mode where it just provides a trickle to counter normal self-discharge.
Usually cheap consumer stuff like this doesn't follow any such algorithm. They have a transformer, rectifier, cap, and resistor. Or probably no resistor. It's crude.
When you do this kind of unregulated charging, you end up with 2 possibilities. One is the charge voltage and rate is high and when the battery finishes it will receive an inordinately high overcharge as time goes on which will over time decrease the battery's performance and life. So you should take it off after you reckon it's charged (voltage and current readings help a LOT in guessing) and not leave it like that for many hours. Or on the other side you may have lower voltage and charge rate, it may take a very long time to charge, 12, 24 hrs, but the overcharge rate after that is not so bad so leaving it on for days will not do much damage. That's what the mfgs usually shoot for.
When it doubt, go with the low charge rate. What do you have to do this with?