How can I delete location sharing text message?

Depending on the situation, and what you are asking…

Delete messages:

https://support.apple.com/guide/iphone/delete-messages-and-attachments-iph2c9c4bfcb/ios

Start or stop sharing locations:

https://support.apple.com/guide/personal-safety/share-or-stop-sharing-your-location-ips05ede4573/web

Using Safety Check:

https://support.apple.com/guide/personal-safety/how-safety-check-works-ips2aad835e1/web

wileyp wrote:

I don’t want to stop sharing my location. I want to delete the text message that says I am.

Does the previously-linked message-deletion procedure not allow that message to be deleted?

Any error messages or diagnostics shown?