first, thank you for your donation. to stop the request, click settings>general and untick the start message.

Just to confirm, are you pointing to the "When Thunderbird launches, show the Start Page in the message area" setting? Well mine is already unticked and I'm still getting the 'donate please' messages. Yes I have donated.

coombshomecare and iamjaydear, thank you for your donations.

Thunderbird Start Page is unrelated to donation appeals which open in a tab. And neither has the means to know whether you have already donated, something that might be resolved in the future but not possible today.