Solomon's Pools is not an Islamic holy site. It has nothing to do with Islam. And at least one of them was undoubtedly built during Maccabean Jewish rule.
Usurpers perform Talmudic rituals at Solomon's Pools
So when Arabs complain about "Talmudic rituals" (meaning, Jewish prayers), for example in the Temple Mount, it is not because they are Jews are desecrating a supposed Islamic holy site.
It is because they are Jews practicing Judaism.
By coincidence, historic photographs of Solomon's Pools were the subject of yesterday's "Israel's Daily Picture" blog.