We must stop meeting like this, people will talk
While Elements does have an option to reduce noise, from PSE menu;
Filter > Noise > Reduce NoiseThis will also remove fine image detail.
There are some settings there to play with, but bear in mind that one is liable to counteract the other, you need to view the areas of concern at 100% to see the effects of the controls.
On these shots, you won't easily see it affecting fine detail though, unlike noise which (at 100%) may stand out like a sore thumb.
However, my recommended solution is Neat Image, a third party bit of software which you can even access from within Elements when needed - it appears at the bottom of the menu list for Filter. It does cost money though and be careful to buy the correct version, you can try the demo version for free.
This is different to what's built in to Elements, because it samples an area of the image with no image content (i.e. a plain shade of grey or colour) and then identifies the noise and subtracts that from the entire image - it can be very effective at removing noise and preserving most of the fine detail.
Here's a thread that explains how to use it.