Probably you're trying to use start.me on a touch device. We disabled this feature on touch devices because it caused other problems.
You can still move bookmarks from one widget to another, though.
- Open Edit mode on both widgets (sending and receiving), by clicking the More options button and selecting Edit.
- Now you can use the directional arrow icon in the upper left corner of the widget to move the widget around
- After moving the bookmark, click Save in the context menu, or the Done button at the bottom.