You can clear out the cache storage of Twitter for iOS

Twitter for iOS has introduced a feature to allow you to manually clear out the cache storage used by the app. This is especially useful if you’re a heavy Twitter user or own a 16G iPhone. 

From the Twitter for iOS app, tap on the “Me” tab. Look for the gear icon beside your profile picture and tap on it. From the popup menu, select “Settings and Privacy” > “Data Usage”.

You can clear out the cache storage of Twitter for iOS

Under Storage section are listing for the cache usage for Media Storage and Web Storage. Tap on it for option to clear out the cache.