Shock leaking after being replaced

I doubt if they would have known the shock was bad and leaking right out of the box, because the piston has not been expanded/contracted until it was installed on the vehicle.
Take it back and show them the shock that is leaking oil and I am sure they will remove it, return it and install a new one.

Little back information. The garage that refitted the original suspension were the same garage that we had used to take it off and replace with coil overs. We got in touch with them today and they are determined that we had never provided them with the dust cover that caused the shock to seize, nor did they realize it was missing and that they had fitted everything we had supplied. Now we did not touch anything inside of the box or the parts they provided us with when they took the suspension off. Also, would they have let us drive out of their workshop without the dust cover let alone supposedly not realized it was missing whilst fitting it? I am not exactly knowledgeable with this stuff so I do not want to go in all guns blazing until I have a good understanding and advice from other mechanics.

So you had them remove the factory parts and install coil over assemblies and put the factory parts in storage. Then the same shop reversed the process and put the original parts back on, correct?
I doubt it had anything to do with the installation. Most shops treat "customer supplied" parts the same way. You bring them in, they install what you brought.
It is more likely it is just a failure, either internal valving or a bad seal. I have seen new parts that did not work right out of the box. It is even possible that while the parts were in storage the piston rod received a ding or even was already defective.

I would see if the dust cover was also missing from the shock on the other side, if not, then they should have known it was supposed to have a dust cover.