Actually, that makes me curious as to the Roman practice on maintaining historic structures. The Romans at many points recycled old monuments, but is this universally the case? Are we in a world where the Romans are repairing the Parthenon? Is it repurposed? Is it only maintained as a sort of park?
IOTL as it usually goes, it often depended on the context and use of the building in question, although overall I would say they fared better than the rest of Europe. To take Athens as an example, the Parthenon was well maintained while it was a church. The Parthenon had burned in the 3rd Century, and it's original roof/interior was long gone, but the rebuilt version by Julian was still in good shape as a church. There's no indication of it being in ruins until the Venetians blew it up in the 17th Century.
Temples that weren't converted into churches were often closed and later recycled for building materials (The Hagia Sophia for example has most of its marble revetment and columns taken from Ephesus). However this doesn't mean that the medieval Romans had no reverance for their Pagan past. Constantinople, as is mentioned numerous times in the Patria was decorated with a massive amount of Pagan statues. The Hippodrome had a massive bronze statues of Herakles by Phidias, the Melitine Gate the Emperors used to enter the Augustaion was decorated with Gorgon heads, the Forum of Constantine contained statues of Apollo/Athena and the Senate House there had bronze doors depicting the battle of the Titans.
Roman authors from this time often had interesting excuses for this preservation of what they would see as a demonic and heathen past. Constantine of Rhodes tried to reconcile the Forum of Constantine's Pagan imagery by claiming that Constantine brought these pagan decorations there to be mocked. He also, seemingly deliberatly, goes out of his way to avoid talking about the massive personification of Constantine as Sol Invictus at the center of the forum. Probably failing to reconcile the pious St. Constantine with this prominent portrait of him.
There were also many legends associated with Pagan statues. A popular one was that if you stared at them for too long something unfortunate might happen to you (one example states that a statue fell on top of someone and killed him, because he stared at it for too long).
In short; the Christian Romans would often preserve historic structures as long as they were given a suitable use/purpose. Even Pagan statues would be preserved and even respected as long as they served a purely decorative/historic purpose and were not worshipped.
