Can we Transgress the prohibition of "Me'ilah" Today?

Yesterday in daf yomi we discussed whether you can transgress the prohibition of "Me'ilah" by misusing stones from the Beit HaMikdash (Me'ilah is the prohibition against using any item designated for the Beit Hamikdash).

This got me thinking about whether / how we should be careful of this prohibition today. For example, if you go to the Batei Machseh Square in the Old City there are some ornate pillars that have been put there on display.

These pillars probably are from the Nea Church which was a large Church that stood during the Byzantine period and lies under the current parking lot and the Batei Machse square (you can see the remains of an Apse from the church outside the current walls).

Because of the ornate nature of these pillars, there is a good reason to believe that they pre-date the construction of the church and were built for a Roman-period building that pre-dated the Church.

Given that the church was built in the 6th Century CE, it is quite probable that the pillars were brought to the site of the Church from the Temple Mount, less than a kilometre away and remains of the Beit Hamikdash would still have been present then. In other words, there is a real possibility that these pillars originally stood in the Beit HaMikdash.

Every time I walk through the square I stop to think about those pillars and try to imagine what they may have seen – the entire history of Jerusalem from standing proudly in the Beit Hamikdash, to be torn to the ground on Tesha B’av, to see the Romans, Byzantines, Muslims, Crusaders, Mamluks, British, Jordanians, and others come and go, to be finally picked up again by the Jews, the same people that lovingly built those pillars more than 2000 years ago.

So here’s my question, if these pillars (or any other artefacts) were part of the Beit Hamikdash, is there a prohibition to make use of them today?

For example, if we take shade or lean against the pillar, are we transgressing the prohibition of Me'ilah?

I’m not a Rav or Halachic authority and have no idea if this is a real Halachic concern, I’m just thinking aloud here…

As we enter the month of Tamuz, may we all merit to see the Yerushalayim and the Beit Hamikdash returned to her former glory.