Praise be to Allah.
The cross is a symbol of the Christians which they venerate because they believe that the Messiah was killed and crucified on it. This is a false belief that was declared false by the Holy Qur’an, which stated that it is a lie and misguidance. Allah, may He be exalted, says (interpretation of the meaning):
“And because of their saying (in boast), ‘We killed Messiah ‘Eesa (Jesus), son of Maryam (Mary), the Messenger of Allah,’ - but they killed him not, nor crucified him, but the resemblance of ‘Eesa (Jesus) was put over another man (and they killed that man), and those who differ therein are full of doubts. They have no (certain) knowledge, they follow nothing but conjecture. For surely; they killed him not (i.e., ‘Eesa (Jesus), son of Maryam (Mary) )”
It was the practice of the Prophet (blessings and peace of Allah be upon him) – as it says in Saheeh al-Bukhaari (5952), in a report from ‘Aa’ishah (may Allah be pleased with her) – that he did not leave anything in his house on which there were crosses, but he would break it and change it.
Based on that, it is not permissible for the Muslims to have crosses on anything in their houses, furnishings or mosques.
And Allah knows best.