The policy has been updated, correct.
If Content is deleted, gains protected status, or is otherwise suspended, withheld, modified, or removed from the Twitter Service (including removal of location information), you will make all reasonable efforts to delete or modify such Content (as applicable) as soon as reasonably possible, and in any case within 24 hours after a request to do so by Twitter or by a Twitter user with regard to their Content.
This is substantially the same guidance provided before, with some additional commentary added around location data etc.
Additionally see section I.C.4:
If your Service will display Content to the public or to end users of your Service, and you do not use Twitter Kit or Twitter for Websites to do so, then you must use the Twitter API to retrieve the most current version of the Content for such display. If Content ceases to be available through the Twitter API, you may not display such Content and must remove it from non-display portions of your Service as soon as reasonably possible.
In both cases you should not be storing Tweets for the long term and then indiscriminately sharing or displaying them in the cases where the content is not public or has been deleted from Twitter. It is indeed very important that you abide by these rules as they are central to the privacy of Twitter's users.
The use of Twitter Kit or Twitter for Websites for display of the content automatically ensures that your service is compliant with the Display Requirements, and with the guidance on not displaying protected or deleted content.