What the saints have said about Islam [cf. What Did the Saints Say about Islam? | 1P5] may assist you in this regard. For example St. John of Damascus’s Critique of Islam (sans references) has a paragraph on how to answer the accusation of idolatry when Christians venerate the cross:
They furthermore accuse us of being idolaters, because we venerate the
cross, which they abominate. And we answer them: ‘How is it, then,
that you rub yourselves against a stone in your Ka’ba and kiss
and embrace it?’ Then some of them say that Abraham had relations with
Agar upon it, but others say that he tied the camel to it, when he was
going to sacrifice Isaac. And we answer them: ‘Since Scripture says
that the mountain was wooded and had trees from which Abraham cut wood
for the holocaust and laid it upon Isaac, and then he left the
asses behind with the two young men, why talk nonsense? For in that
place neither is it thick with trees nor is there passage for asses.’
And they are embarrassed, but they still assert that the stone is
Abraham’s. Then we say: ‘Let it be Abraham’s, as you so foolishly say.
Then, just because Abraham had relations with a woman on it or tied a
camel to it, you are not ashamed to kiss it, yet you blame us for
venerating the cross of Christ by which the power of the demons and
the deceit of the Devil was destroyed.’ This stone that they talk
about is a head of that Aphrodite whom they used to worship and whom
they called Khabár. Even to the present day, traces of the carving are
visible on it to careful observers.
As regards 'I want to present it in a way that answers the question correctly, but also is stated in a way that bridges the two religions and doesn't cause a rift in administration' the Church and Scipture teaches that we have to speak the truth, but with Charity. With the help of God and knowing your audience, you have to figure the how.
Perhaps a modern resource: Franciscan University Presents: Catholics and Islam | Franciscan University of Steubenville.