bulldog 500 deluxe anti grind

What you show will work fine for anti-grind. 

You could also use the blue/black Ignition3 wire (H7/1) for the anit-grind control without having to change programming.  You may also connect the orange ground when armed (H7/10) to the same control wire, giving you a starter kill along with anti-grind.   

If you choose to add the starter kill functionality, and there is nothing else wired to either the control wire of your choice or the orange ground when armed, you can directly connect these to each other, and to your relay.   If you are using either of these wires for another function (i.e., bypass, sensor enable, etc.) then you would use a diode (such as a 1N4001)  in each line and connect the banded end of the diode to the Bulldog signal, and then tie both unbanded ends of the diodes together and also to the relay coil. 

I just realized you show the relay tied to +12V.    You may want to tie this to the IGN wire of your remote start.  This will avoid current draw while the car is off--this is particularly important if you do decide to add starter kill.

To be clear, you tied the relay to IGN instead of 12V, correct?  You would not want to connect 12V to IGN...