If you'd like to get rid of your 1-star characters, go to your Roster and tap on the "scrap" button. This will take you to a screen where you can select some, or all, of your 1-star characters to scrap.

Once you scrap them, you'll be rewarded with Scrap Tokens and Goo. You can then exchange Scrap Tokens in the Scrap part of Bob's Store for Great or Excellent Shards.