What is the proper way to dispose of obsolete and worn out battery backups?

Call your town or city hall and see if there is a recycling center available. Do not dispose of the battery in your regular trash--in fact, many towns/cities have made this illegal due to the danger posed by disposing on electronics.

Bring them in to the Hazardous Waste center. They dispose of them properly. At least that's the way it is here in Ontario, where are you from?

Check with Home Depot's or Lowe or best buy they all have battery recycling bins.