GSam has been one of the few great unobtrusive apps for me.
If you can post a screenshot of your Battery usage, you can get more specific advice.
I take it App Analyser is specific to the LG and your G3, I am not familiar with it.
I don't see from your shot where it's using battery, just data.
GSam barely registers at all on my Motorola or Samsung Battery usage.
You asked the same question on the G3 forum and it's not great to compete with similar responses elsewhere.