Not sure if this is your problem. My '07 TCH owner's manual states:
A warning buzzer may sound when:
The key is brought into the cabin after the trunk is opened, and then the trunk is closed -- Doesn't apply to your problem.
The key is near the trunk when the trunk is closed. -- Possibility.
The buzzer may sound even when the key is not in the trunk. This does not indicate a problem. However, under these circumstances, the trunk cannot be opened using the smart key system. Open the trunk using other methods.
I suggest you try this:
Open trunk, get rid of ALL keys, close trunk. Then retrieve one key and see if it will allow you to open the trunk.
Again, this is just a suggestion. Not sure it it is really your problem.
BTW, welcome to the Camry Hybrid world.