You can make a grid with square sprites and use "Pick nearest" to find the nearest cell.
Or use a tilemap, it has SnapX and SnapY expressions.
Or you can do it with math. Say your grid cells are 10*10px. And player drops a piece at x=77, y=22
Use these formulas to find the nearest cell:
nearestX = (round(x/10)*10)=80
nearestY = (round(y/10)*10)=20
Once you know the destination coordinates, you can move your piece there using a behavior like MoveTo or LiteTween.
Or without any behaviors:
On every tick
Piece set x to lerp(piece.x, destinationX, dt*4)
Piece set y to lerp(piece.y, destinationY, dt*4)