Hi
Welcome to Frog Forum

I'm sorry.........this is a wound.
It is at the very tip of the 'tailbone'.
This could have been caused by pressure against the area too long.
Did the frog get stuck behind something?

You can pull the background out !!!!! IMO - trash it!
They would prefer to sleep on the glass

How were they shipped to you ?

They are VERY susceptible to infections if there is a break in their skin.
This frog needs a vet, and antibiotics to be applied to that spot. Sorry

In the meantime....You could get neosporin ( from a pharmacy) WITHOUT pain reliever.
Pain reliever will kill your frog.
Plain neo will help to begin to heal the area until you can speak to a herp vet.
Apply the neo - very - gently- with a clean Q-tip, while the frog is sleeping.

http://www.frogforum.net/tree-frogs/...-prepared.html
( you could email this vet? ) you can pay for medication via a credit card- send the photos

http://www.frogforum.net/general-dis...n-juchems.html

You should contact the person you purchased the frog from as well!

The " opening and closing " of their mouths could be shedding ? but could also be the a result of too high a temp and humidity!
They typically shed right when they wake up for the night... you see them wiping their face.

This is shedding:
https://www.youtube.com/watch?v=s50VrErCPWs

care sheet: ( see temp and humidity parameters )
Frog Forum - Red-Eyed Leaf Frog/Red Eyed Tree Frog Care - Agalychnis callidryas

Seriously, considering separating the frogs ...establish a separate quarantine ( QT) enclosure for each of them:

http://www.frogforum.net/general-dis...uarantine.html
http://www.frogforum.net/tree-frogs/...-supplies.html

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They can take days to adjust. Cover three sides of the tank with a dark cloth, keep them in a very quiet area.
They should have complete darkness at night.

Don' forget their soaking dish: chin deep/ de-chlorinated water ONLY/ clean the dish daily in hop tap water.
( a ceramic plant saucer or regular saucer ) or any really shallow flat dish- even a sandwich plate will do

Feed them small crickets for now until you know ( by counting crickets) or have witness them eating
They do well with bowl feeding ( do a FF search re bowl feeding )
* see care sheet for calcium and vit supplements

Please keep us posted.