Is the mortar on the left level with the boards? (Stupid question I know as it looks it bit just checking)
Also, were you planning for the boards to butt up to the hearth?
Easily and cheaply would be to build up a bit of trim with timber as a hearth surround and paint it a suitable colour for the room (black or white I guess). It could also mask the mortar under the overhang of the hearth. Other options:
Less cheaply would be to not go to bare boards.
Less cheaply and easily would be to extend the hearth.
And less easily would be to take a chisel to the mortar and see if you can do anything with it but you'd still need to build timber up to it!