Fitting a grid to points in a 2d space
You could represent the grid with 5 parameters:


(x0, y0) to represent the offset from your image origin to the grid
origin 
(xs, ys) to represent a multiplication factor from your image
plane to your grid plane. If your grid is spaced apart every 100
pixels on your image plane, these values might be 100,100 
theta to
represent the rotation of the grid


You could fit the grid to point in image by varying these 5 parameters and optimize these parameters by calculating a cost function at each step. 

An example cost function would be the total Euclidean distance between known point and grid points. The grid parameters that best overlap your given point should represent an optimal solution in most cases, especially in cases where you have several "correct points" and few of the "outlier points".

For efficiency you could ensure that your x0 value is [0,xs] and your y0 is [0,ys]. Since it sounds like you have a guess for the size of your grid, you could input a decent guess for xs and ys and also constrain these values from changing too much.