Searching for specific messages in GroupMe chats is only available on mobile.
To search your chats:
Go to the Chat list.
Tip: On iPad, if you don't have your list of chats on the side, tap Chat at the top of the screen.
Either Swipe down or tap the Search icon.
Type your search terms in the Search messages field.
Results are displayed as you type. Select a result from the list to go directly to that message.