SHUTTING DOWN on 16 August
This app is going to be permanently removed due to Twitter changing their API and preventing access to DMs older than 30 days.

View your old DMs and delete them from Twitter

The app will ask for permission to "Access your direct messages".
I will not store, or share your data, but always revoke permissions when you're done.

Note that this app will also ask for some permissions it doesn't need such as "posting Tweets for you".
This is unavoidable with Twitter's permission model. Access to DMs provides access to these things too.