Move the hand grip toward the switch block to take up the play but make sure you have the large plastic washer which goes between the grip and the block.If it is a fixed grip to the tube like suzuki for eg then the only other thing is get a couple of the large plstic woshers to take up the space so you get less movement just make sure you do have some movement though because the last thing you want is for the throttle to stick and turn into a cruise control when you least expect it.
You will find this is common on most bikes .
The only place where you should have grease is on the bar so the throttle tube doesn't run dry and even then only a smear
best thing to use is sewing machine oil and then you only need say a drop or two so the tube has lubricant.
Safest bet by far after all that is to get used to it atleast you know it won't sick