Grading: Its chain is da'if (weak).
Defect ('illah): This is because of the weakness of Layth (Ibn Abi Sulaym), whose memory deteriorated; moreover, 'Ali bin Abdullah bin 'Abbas did not live in the time of his grandfather al-'Abbas (may Allah be pleased with him), so this report is also "mursal" (disconnected).

Details of the narration: This narration is found in Abdullah bin Ahmad's "Fada'il al-Sahabah" (1825), and he added: "So he sent back two of them, and we used to think that he sent them back only because they were children of fornication."

Reference / Source: It was recorded by Ibn Sa'd 4/ 27, and through him by Ibn 'Asakir in "Tarikh Dimashq" 26/ 376, from Abu Nu'aym al-Fadl bin Dukayn with this same chain, but without the above-mentioned addition (about the children of fornication).

Reference / Source: It was recorded by Ibn Abi 'Asim in "al-Ahad wa al-Mathani" (353) via Sa'id bin Maslamah, from Layth, from Mujahid.
Technical note: He made it a statement of Mujahid and did not take it any further (to a Companion)!