Ok, try this.
- Select your rectangle.
- Go
Object > Expand Appearance
.
- Now select one background 'tile' from the rectangle's background and go
Select > Same > Fill & Stroke
to select all of the background tiles.
- Hit Delete.
Alternatively, use one of Illustrator's built-in grid pattern swatches, which have no background colour. In the Swatches panel, click the drop-down and go Open Swatch Library > Patterns > Basic Graphics
and you'll find a whole heap of grids. Or, create your own pattern tile and convert that into a pattern swatch (simply make something, group it and drag it into the Swatches panel).