The architecture is Greco-Roman, with all the usual attributes. But was it really built in antiquity? It was discovered in the early 19th Century (supposedly), but became a popular tourist destination only in the 1980's. There's sand from abrasive blasting all over the place. Some tool-carrying locals are always fussing inside. Some people have suggested that the whole thing was built as a set for the Indiana Jones movie. Is there any proof that it's genuine?
That the whole complex is the ancient Petra is evidenced by the ancient Nabatean and Roman tombs discovered there, and location of the ancient Petra is known, and it is mentioned in the ancient texts. See the picture of these tombs in the end if this article: https://en.wikipedia.org/wiki/Petra#Byzantine_era_.E2.80.93_decline There is no doubt that a lot of restoration was done there since the discovery in 1812. How faithful is the restoration of the particular temple Al Khazneh you are asking about can be discussed but that the whole thing is genuine, there is no doubt.
Actually many old monuments were restored and rebuilt many times, and do not look nowadays the same way they looked in antiquity. For example, the Great Wall of China, as shown to the tourists and reproduced on so many pictures, is a 20s century reconstruction. The non-restored parts look more like the Hadrian wall in England and other Roman walls in Europe: some people do not notice when they walk over them.