Jafer,
Why would you want to give away your money even if the address or letter is legit? All of mine were legit contacts and I stayed dark. The layout of the letter is the same standard tactic these agencies use. Yours is not special. They all demand payment, they all show the image to make their claim. Remember this is a claim by someone, not a legal order or judgment against you.
In regard to someone else designing your website, doesn't matter, you are the owner of the site which makes you responsible party. Not to be disrespectful, but the tone of your letter has a great deal of worry emphasized. Perhaps you are unable to withstand their aggressive tactics to scare you into paying when you aren't even sure if they actually represent the image holder.
If you are uncomfortable or the events give you a gut ache, then by all means pay it. Just remember when you do something like that, you play into the hands of these image trolls. You are a number and it is a numbers game. If you succumb, then you were part of the low hanging fruit for them to go after. I just heard from my troll again today after her not sending anything for over 3 weeks. To give you an example of how you are just a number not worth notating important facts, in her latest letter to me she states the image in question is still up, yet in her letter dated first week in January, she states the image is down, but I still owe the $300.00. I am no one to them but an easy mark if I were to give in.
Plus the kicker is I owned the image in question purchased through iStock, but they sold to Getty and my license for this image mysteriously disappeared along with a few others. What you should realize is the images may have been Royalty Free or not, can't say, but as has happened with me what was once a Royalty Free image became magically a Rights Managed image returned to the private party that may or may not have had a beef with Getty taking over iStock and decided to remove the licensing they had with them. Who knows, but I won't be a pawn in their extortion game.
As in the past with these trolls, the letters get further apart as this one did and they will continue to do so, I am confident. The dollar amount they are seeking is less than it would be to hire a legal rep, travel to my jurisdiction and file a lawsuit. It is about weighing likelihoods with critical thinking. Do your research as you have been doing and then decide what you can handle and cannot handle. If you lose sleep over this stuff, then pay. If you can gut it out and await the next troll letter and simply store copies without responding, then do that. It is really about you and only you can decide what makes you sleep at night.
did some editing with time frames, not to mislead, but to not place exact dates due to this site is known to be monitored by these image trolls.