Not sure if this will be any help but I'll try to explain how I solved my grid issue.
The game I'm making is a chess-based puzzle game for a school project and the way I made grid movement possible is by aligning sprites in the background to form a grid. I've implemented a system that changes the specific grid sprites to active for the player to be able to go to that sprite, depending on what kind of move set the player chose. That works by spawning sprites on top of the tiles and the just kind of checking if the grid and the spawned sprites overlap.
I included screenshots.
I don't know if this is a proper solution to this issue because this is literally my first ever time working with Construct, let alone making a game.
If you are looking for a way to make it turn-based, then I'm not of any help because I'll have to tackle that problem myself too.
Hope this is in any way useful.