To delete a field marker or line you'll need to go to the Map Legend on the left side of the screen.  Click on the type of asset you want to delete (fields, markers or lines) to reveal all the assets you've created as well as a pencil icon in the top right.  When you click the pencil (edit) icon, you will be in "edit mode." Now you can click on the trash can next to the asset to delete it; remember to click the pencil icon once you are done to switch "edit mode" off.