Contacts in Text Request cannot be deleted unless they have no prior message history (for compliance reasons).
Deleting a contact is useful if you added a number that is either invalid, disconnected, or a landline number that you could not previously send a message to.
You can delete a contact by selecting its number, then selecting Delete Contact in the Details window that opens.
If you have a contact with existing message history that you’d no longer like to message, you can Archive it. Archived contacts will be removed from auto-fill suggestions and the conversations menu. You will not see them unless you send them a message later, or choose to view Archived Contacts in your contact filter. Archived contacts are automatically activated if a message is sent to or received from them.