Jesus referred to his quote from Psalm 35:19 as "written in their Law" (ὁ ⸂ἐν τῷ νόμῳ αὐτῶν γεγραμμένος, NA28). Why did Jesus refer to the scriptures as their law instead of God's.
But the word that is written in their Law must be fulfilled: ‘They hated me without a cause.’ (John 15:25, ESV)
Let not those rejoice over me who are wrongfully my foes, and let not those wink the eye who hate me without cause. (Psalm 35:19, ESV)
Jesus was not talking to disciples who did not accept the complete Tanakh as authoritative.
Although he doesn't directly address why Jesus used "their," this is how Eli Lizorkin-Eyzenberg addresses this subject:
21 But all these things they will do to you on account of my name, because they do not know him who sent me. 22 If I had not come and spoken to them, they would not have been guilty of sin, but now they have no excuse for their sin. 23 Whoever hates me hates my Father also. 24 If I had not done among them the works that no one else did, they would not be guilty of sin, but now they have seen and hated both me and my Father. 25 But the word that is written in their Law must be fulfilled: ‘They hated me without a cause.’
It is still clear that these particular words of Jesus belong in a particular historical setting. The opposition by the Ioudaioi [Jewish leadership] and in particular, by those in leadership, the evil shepherds of Israel, is clearly in view. The summarizing phrase in verse 25: “they hated me without a cause,” referring to the persecution and suffering of Jesus, is a direct reference to several of the Psalms of Lament. In Psalm 35: 1-8 we read:
“Contend, O LORD, with those who contend with me; fight against those who fight against me! …Say to my soul, “I am your salvation!” Let them be put to shame and dishonor who seek after my life! …Let their way be dark and slippery, with the angel of the LORD pursuing them! For without cause they hid their net for me; without cause they dug a pit for my life.”
While in Psalm 69: 1-4 we read:
“Save me, O God! For the waters have come up to my neck. I sink in deep mire, where there is no foothold; I have come into deep waters, and the flood sweeps over me. I am weary with my crying out; my throat is parched. My eyes grow dim with waiting for my God. More in number than the hairs of my head are those who hate me without cause…”
This is the case throughout the Gospel of John. The Ioudaioi launched a full attack against Jesus, hating him without a justified cause. And this is the case with the world - it has no justified reason to oppose God, but it hates Him and everyone who belongs to Him. -- Lizorkin-Eyzenberg, Eli. The Jewish Gospel of John: Discovering Jesus, King of All Israel (pp. 219-221). Jewish Studies for Christians. Kindle Edition.