The only problem is that the facts don't support that claim.
Israeli archaeologists not only eagerly find Muslim sites, but Israel preserves them - even when they are near Jewish historic sites.
Here's a new example of one of the world's oldest mosques, just discovered by a Jewish archaeologist from Hebrew University:
When Islam started to spread in the seventh century, mosques were built across the Middle East, and many have endured to this day as holy places and pilgrimage sites; the most famous are in Mecca, Medina, Jerusalem, Cairo and Basra. Now it looks like Tiberias in northern Israel may be joining the list – excavations in recent years have uncovered an older layer of the city’s ancient mosque.Katia Cytryn-Silverman of the Hebrew University, who is overseeing the dig, says this is the oldest mosque in the world that can be excavated; most ancient mosques are still being used for their original purpose.The Al-Juma (Friday) Mosque is in the south of Tiberias at the foot of Mount Berenice; the city itself is on the shore of the Kinneret, the Sea of Galilee. Before Cytryn-Silverman began excavating there 11 years ago, scholars believed that the structure at the center of the site was a marketplace from the Byzantine period. Cytryn-Silverman discovered that it was a mosque from the eighth century in the early Islamic period.But findings in recent years have shown that under this structure is an even older mosque, dating to the seventh century. Cytryn-Silverman notes that there aren’t many chances to excavate ancient mosques because, in most cases, other mosques were later built on top of them. Such is the case with the mosque in Fustat, currently part of old Cairo and Egypt's first capital under Muslim rule.
Israelis have found and preserved some of the most important Islamic archaeological sites. And that fat simply doesn't fit the lies of the haters.
(h/t Yoel)