When you press the Composer button in the menu, you will see a tree view of a Touchgram.
A new message shows a simple, single page like this.
If you come back to a draft Touchgram after closing the window, you might see a lot more details in the tree.
On the expander bar there is a little Close button, a circled-x which only appears in the Expanded view.
This is part of the standard iMessage interface so Touchgram cannot do anything about it.
Be very careful about hitting this Close.
The close will cancel the current message you are editing and...