In Wordscraper, you cannot delete  a custom board but you may override it. The steps to override a custom board are as follows;
  1. Open Wordscraper and select Host Table option from the New Game menu.
  2. Select the board type as Custom.
  3. Select the option Load a Design.
  4. In it click on the slot that you have designed which you would want to overwrite.
  5. Click on the edit option which is to the bottom-left of the board.
  6. Now, you will be able to make changes for your board.
  7. Once you are done, you may click on Next option and save this board as a new slot if you like.
  8. Then,you may start your game.

In this manner, you may override a custom board.