The sugya discusses whether the kedusha of mikdash and yerushalayim (to the exclusion of kedushas ha'aretz - see tosafos) is still present nowadays. The Rambam (Hil. Beis HaBechira 6:14) writes that the kedusha of the shechina cannot become batul. The sugya is too large to discuss in this forum - see here for a shiur on kedushas hamikdash. But, here are some short points:
1. The Gemara in Avoda Zara 52b says that the kedusha of the mizbei'ach was lost by the Greeks based on the concept of ובאו בה פריצים וחיללוה - and that is how they were able to make it assur as avoda zara even though it didn't belong to them. Why wasn't the kedusha of Yerushalayim and the Mikdash also lost based on this concept? The Maharam Shik (mitzvah 255) explains that the concept worked to make remove kedusha from the structure but not from the place. The kedusha of the place is kedusha of shechina, as the rambam writes, and can't be violated.
2. Since during the time of Ezra they didn't have the ability to restore the kedusha to the mikdash and Yerushalayim (since they didn't have urim v'tumim or a king), why does the gemara say that those who went up from the go'leh sanctified har hazeisim - they couldn't truly restore the kedusha so why bother doing anything? Tosafos writes that the question is even greater. By going through the motions of sanctification, it made it seem to the amei ha'aretz that it had kedusha and they ate kodshim there. Why did the b'nei ha'goleh do something that was a stumbling block for people? Tosafos explains - כדי שימסרו עצמם עליה יותר כשיש בה שם קדושה. Tosafos is making a fascinating point. It was necessary for the Jews to maintain of har ha'zeisim for security purposes, because it would be a strategic location from which to capture Jerusalem, as the gemara writes. The b'nei go'leh were afraid that if it wasn't perceived as having kedushas yerushalayim, the people would not be moser nefesh to maintain control of har ha'zeisim. Therefore, they pretended to sanctify it even though they didn't have the power to truly give it kedusha, to give the perception of it being part of the city, in order to maintain the security of Jerusalem.