I would recommend removing "7" from the board at all. The easiest opening move is to just start clicking all the 7s (since that guarantees you all multiples of 7 until you run out of 7s). This strategy requires 0-thinking and is a bit tedious. If the board has no 7's on it, you're required to add from the get-go. EDIT: Also, very fun little game. Thanks for sharing!
That only works until you hit 21, thats a multiple of 3 and you lose.
I hit three 7s and scored 21 points. Then four and got 28 points.