Short Answer: We don't know, there aren't any available sources.

Expanding on the topic, considering you're asking about Western/Latin accounts, the closest thing we would have is an account by Arculf, a bishop from Gaul that visited Jerusalem for 9 months in the 670's AD.

While in Jerusalem, he mentions:

"In that famous place where once stood the magnificently constructed Temple, near the eastern wall, the Saracens now frequent a rectangular house of prayer which they have built in a crude manner, constructing it from raised planks and large beams over some remains of ruins. This house can, as it is said, accommodate at least 3000 people."

• excerpt taken from Robert G. Hoyland's fantastic work Seeing Islam As Others Saw It: A Survey and Evaluation of Christian, Jewish and Zoroastrian Writings on Early Islam

If you're looking for overall Christian attitudes towards the Arab conquests, you'll find more in that book. Sophronius, the Patriarch of Jerusalem from 634-638 AD, writes quite explicitly of the Arab conquest of Jerusalem.