Completely delete an app and the app's cache from iPad
App settings aren't cached between installations. Either there's a bug in your app's settings, which it pulls from their API's through their website, or perhaps they have iCloud settings stored.

In the first case you should contact Trello about it or try removing and then re-adding the buggy content through the web version. If the latter is the case, go to Settings, iCloud, Storage, Manage Storage and find Trello. Then press Edit and Delete All.