yeah, just install the tickets
basically what happened, in a "simple" way:
there is game ticket and game data
- tickets serve both the purpose of telling the 3DS the game and installed (and thus, showing a nice icon on your 3DS menu), and to check if you really have the right to use it (cfw bypass that)
tickets are located in your nand
- game data, well, its game data, its, you know, stuff, and its located on your sd card (well except for dsiware, they are on nand,, thats why you are limited to, like, 40 dsiware title max)
when you restore a nand which dont have the tickets, the game is not recognized as installed by your 3DS, BUT the data management software can still see and identify the data stored on your sd card, it just cant launch it
so, by simply reinstalling the ticket, the games should work again
and if you try to fully reinstall the game on top of what you have for the moment IT WILL ERASE YOUR SAVES, so just install tickets, dont reinstall cia