Two suggestions are given by the Gemara to explain why we would not accept such converts; it is either because of “Solomon’s slaves,” or because of “the daughters of Jerusalem.”
The Gemara explains that both of these positions are based on a ruling (which is not accepted as the halakha) that a child born from a relationship between a non-Jewish man and a Jewish woman is a mamzer, an individual who is considered Jewish but is limited in who he can marry. The case of Solomon’s slaves is described in I Melakhim (9:18), where we learn that King Solomon had non-Jewish slaves who built the city of Tadmor. Apparently these slaves were known to have taken Jewish women as wives, and there was reason to suspect that their descendants were still living in that city. The case of the daughters of Jerusalem is explained by Rabba bar bar Hana. Based on the passage in Eicha (5:11), he suggests that when the first Temple was destroyed and the city of Jerusalem sacked, although most of the attackers looked to take the spoils of gold and silver, some turned to the daughters of Jerusalem.
The city of Tadmor was an oasis in the Syrian Desert. For many years it was a central business district and important crossroads between Syria, Arabia and Babylon (see map). The city was sometimes called Tarmod, but it is best known by the name Palmyra, for the many palm trees that grew there.