On average, the majority of Brita pitcher filters have a capacity of 40 gallons while on-tap filters are approximately 100 gallons. You'll be surprised how many gallons of water you go through in a month and replacing those plastic filters can produce plenty of extra trash in your local landfill despite your good intentions not purchasing any more water bottles.
Visiting Brita's recycling page or simply going directly to Preserve Product's "Gimme 5 locations" to locate a recycling center nearest you. Simply collect them in a small bag/box and drop the filters off at allocated centers. The recycling crew will take care of the rest.
Hopefully that'll curb the number of filters you're currently throwing in the trash and make you feel a little bit better about drinking cleaner water while being sensible to your environment.