You open it up by unscrewing it counterclockwise, where the black o-ring is. Clean it, check the o-ring, replace if necessary (generic part) and put some silicone grease on before reassembly.
This is not a water filter, just a strainer to protect the pump from debris in the tank. If you want filtering of drinking water, fit an activated charcoal filter under the sink with a separate tap. I think there's a thread or two somewhere around here on that subject, if not, look up Britaly on Youtube, they've done a video on it.
Treatment tabs are usually chlorine, they kill bacteria but do not improve taste, and if you overdose them you get a icky chlorine taste too.