As a Member of a Gaggle, you control what messages that you share and what messages that you don't. In the case where you select the "No Thanks" option, that message can no longer be shared by you. Using the "No Thanks" button is permanent, so if you have any doubts, you can either share the message or leave it as as and revisit it later. The message will stay available to you for the duration that the Gaggle Manager has set for it.
Saying "No Thanks" to a message will eliminate it from your ability to share and will remove the message from your message list the next time you refresh. You can also provide feedback when you say "No Thanks" by clicking on the link that appears after you click "No Thanks".
This will bring up a form for you to provide feedback to the Gaggle Manager on why you did not share the message. This information is sent to the Manager as anonymous, so please feel free to be candid and constructive.