Is this delivery report has been requested notification interfering with your phone's functionality?
Are you experiencing issues while sending/receiving text messages?
What application are you using to send/receive text messages?
I trust that once more details are posted our forum members and our Social Media team will be able to better address your concerns.
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SMS and MMS delivery acknowledgements are defaulted to OFF out of the box for all devices. If you want them just open the messaging client, go to settings and enable them for both SMS and MMS. They are separate settings. Then it seems that the Galaxy does not have an icon next to the message the indicates either SENT or RECEIVED BY THE RECIPIENT :-( . So for each message just press the message and select "View Message Details". That should do it.