I am receiving unwanted , sometimes obscene, messages added to previous legitimate messages. How do I deal with this?

Hello 43_TG,

Thank you for reaching out in Apple Support Communities. For unwanted messages, you can report it to Apple. Here's how:

Report spam or junk messages

When you use iMessage, you can report spam messages to Apple. Depending on your carrier and country or region, you can also report spam you receive with SMS and MMS.

In the list of messages, touch and hold the spam message, then tap Report Junk. Or, if you’ve opened the message, scroll to the bottom of the message, tap Report Junk, then tap Delete and Report Junk.

The sender’s information and the message are sent to Apple, and the message is permanently deleted from your device.

Note: Reporting junk or spam doesn’t prevent the sender from sending messages, but you can block the number to stop receiving them.

If you don’t see the option to report spam or junk messages you receive with SMS or MMS, contact your carrier. See the Apple Support article Wireless carrier support and features for iPhone.

Following these steps can help and is outlined in this article: Block, filter, and report messages on iPhone - Apple Support

Kind regards.