The key question is "delete from where?".
The Carbonite app will let you backup all messages or just the ones that you select.
If you just want to delete the messages from your phone, go into your SMS app and select those messages then use the 3-dot menu to delete them.
When viewing an individual conversation, you can normally select the individual messages to delete.
When viewing the list of conversations, you can normally select and delete the whole conversation.
For more details:
Which phone?
Which version of android?
Which carrier?
Which SMS app?