This article is related to Why does BlackLight display duplicate messages in black text and also in red italicized text?
If you want BlackLight to only show active text messages and not include the deleted recovered messages, there is an easy solution using the View Filter.
1- In 'Communication' view, 'Messages' subview, click on the View Filter icon 
in the upper right corner to reveal the Filter.
2- Next click on the + button to add a Filter condition. Then select from the drop down menu options - 'Deleted Record' is 'False'.
3- Click on the Apply button to run the filter.
Note: There are two ways you can tell whether a filter is applied in the current view:
1) The View Filter icon turns green.
2) At the bottom of the application window, the Status Bar displays the new message count and the word Filtered.