To remove the pulp: be prepared to get messy! You can do this a number of ways, but I simply peeled off a couple sections of the skin (which is hard to do if you have really ripe fruit), dug the seeds out, then used a spoon to get the remaining pulp. See the "Recipe Notes" section for a link to the Ohio Pawpaw Growers Association suggestions. You should have about 1-1/4 cups of pulp.
Add the pulp and remaining ingredients to a blender and process until fully pureed, about 1-2 minutes, scraping down the sides as necessary. Taste and adjust seasoning as needed (you may want to consider an extra pinch of salt or lime zest). Pour into popsicle molds (I use the Zoku Classic Pop Molds, which hold about 3 oz each) and freeze overnight.