How do I get Resolve to ignore a green object held by the talent in front of the green screen, in other words, allow this to pass through without change? I assume I use a power window but am not sure how to proceed from there.
Assuming you used an eyedropper secondary qualification, you create a roto-shape power window and subtract it from the HSL qualifier by using the invert controls found on the right-hand side of the power window dialog. From there: tracking, clip/frame animation, blurring, feathering, adding more tracked and animated power windows if the foreground object changes shape in an organic way... (you are building a puppet)
"I always pass on free advice -- its never of any use to me" Oscar Wilde.
And in addition to Joe's excellent answer above: you need to use a GARBAGE MATTE to handle the occlusion (the unwanted element passing in front or near your keyed image). A tracked power window can do this. Check out pages 2215-2218 of the Resolve 15 manual.