What phone, what texting app, do you want to delete an entire string or just old messages within a string?
On my Moto X using Hangouts, I can easily delete an entire string using one of 2 methods:
- Long-press on the entry for the string and tap the trash can, this will also allow me to delete multiple strings at a time if I select them
- Tap on a string to open it then tap the menu icon (3 dots but some devices have a capacitive key for menu) and then select delete
You can also delete individual messages within a string by long-pressing on a message and selecting delete from the pop-up menu.