There is no Options dialog for setting the display grid (drawing canvas) colors in AutoCAD Web. But you can set all colors of the user interface using environment variables through the LISP interface.
So you can e.g. set all major grid lines in a lighter, more prominent color (in the dark model space) for the base 2D grid, with:
(setenv "2D Model grid major lines color" "9996932")
Just paste this into your AutoCAD web command line prompt and toggle the grid off and on (F7).
You may then switch the major lines back to the default color with:
(setenv "2D Model grid major lines color" "6901577")
Similarly, you can change the color of minor lines in your grid, with:
(setenv "2D Model grid minor lines color" "8878450")
And go back to default with:
(setenv "2D Model grid minor lines color" "4732722")
For the layout grids (white background), use the variables:
(setenv "Layout grid major lines color" "15380637")
(this is the default color)
and:
(setenv "Layout grid minor lines color" "15380637")
(this is the default color)
The individual custom color codes (long numbers) can be generated for any color tint e.g. using the Color conversion tool - choose a color and then copy/paste the gray italic "Long code" under R/G/B.
These settings work also in standard AutoCAD and AutoCAD LT, incl. in the Mac versions.