Once the "ears" past the edge, it should be easy to slide the tray the rest of the way out.

Note the battery type carefully: It is a ML2032, which is rechargeable. This is NOT the same as a CR2032, which is not rechargeable. Do Not replace with CR2032, as the solar panels will attempt to charge it.

Note the proper orientation of the battery (see picture), positive + symbol facing towards bottom. Negative side facing keys.

To make it easier to remove the battery in the future, trim the ears slightly or slice some notches in the plastic "springs" to weaken them a little.