Aye, getting rid of the grid is the most important part when dealing with tiles, especially grass.
The best way to do this is use more then one time, and alter things slightly with the tiles as you work. You'd be surprised how one sligh movement of a pixel in a tile can change the look when tiled.
Here is an edit I did with your tile. I took the "chunk" of grass, then copied and pasted it into the large "empty" spot that's being shown in the grid.
Though this isn't your answer, and my edit doesn't justify what a good tiled grass should look like. All I'm saying is fill in that empty space, and it changes the look a lot, in a positive way. When you focus too much on the center of the tile, and ignore the outer parts of the tile, you end up with that "grid" result. The best thing to do when making tiles that will repeat themselves a lot like grass is to treat every space of the tile the same.