First I have to admire the boldness with which this Hindu Quora poster, an "expert in Ottoman History" according to his bio, quotes from The Foundation of the Ottoman Empire (1916), by a Christian journalist who bemoans the failure of his religion to convert the Seljuks.
It is amusing how seriously he has misread this old source. The Quora user writes (or reposts a meme saying that) "Ertugrul and his son Osman were Pagans. When they sacked Mosul in 1286, they made no distinction between Muslim and Christian."
But the quotation he uses to claim this does not mention Etrugrul and Osman, only "Turks and Turcomans". The author of The Foundation of the Ottoman Empire is not including Ertuğrul and Osman in any activity in 1286. Just two pages later, he writes:
It was the conversion of Osman and his tribe which gave birth to the Osmanli people, because it welded into one race the various elements living in the north western corner of Asia Minor. The new faith gave them a raison d'être This conversion ... is the explanation of the activity of Osman after 1290, as in sharp contrast with the preceding fifty years of easy, slothful existence at Sugut.
Ertogrul and Osman, village chieftain at Sugut, had lived the life of a simple, pastoral folk, with no ambition beyond the horizon of their little village. No record exists of any battle fought, of any conquest made. Turks had already made their appearance in raids against the coast cities of Asia Minor upon the islands of the Ægaean Sea, and even in the Balkan peninsula. But they were not the Turks of Osman. Until the students of the later Byzantine Empire, and of the Italian commercial cities in their relations with the Levant, make a clear distinction between Turk and Osmanli there will always be confusion upon this point. Ertogrul had about four hundred fighting men. There is no reason to believe that Osman had more. His relations with his neighbours were those of perfect amity. There is no question of believer and unbeliever.
Suddenly we find Osman attacking his neighbours and capturing their castles. During the decade from 1290 to 1300 he extends his boundaries until he comes into contact with the Byzantines. His four hundred warriors grow to four thousand...
The author attributes this sudden expansion to Osman's conversion to Islam, but in a footnote on p.25 he acknowledges that some sources describe Ertuğrul himself as the convert.
You may notice that this not only contradicts the Quora user, but in describing Ertuğrul as an originally peaceful Muslim whose religion compels him to fight for divine justice, it is surprisingly similar to the plot of the drama Diriliş: Ertuğrul. As I mentioned in the answer to "Were Ertugrul and his son Osman pagans?," we don't know anything about the historical Ertuğrul; everything comes from unreliable Ottoman hagiography, which is the conscious basis of the fantasy drama. The Foundation of the Ottoman Empire accepts this hagiography at face value and rewrites it from a Christian perspective. Hence the "Turks and Turcomans" that the Quora user is referencing are basically the tribal enemies of the fictional hero Ertuğrul as seen on TV, but he has sadly misread the fiction and attributed the raid to Ertuğrul himself.
I guess none of this answers the question, so I will add that in historical fact, the sack of Mosul was unrelated to Osman. Nothing is known about Osman before a Byzantine chronicle reports he won a victory against them in 1301. According to Osman's Dream, the Byzantines tried to make amends by arranging a marriage between one of their princesses and a man from Osman's general khanate, so it doesn't seem like they considered Osman to be a bloodthirsty maniac. His forces won their next victory in 1326, again taking a Byzantine city; it doesn't seem a pillage or slaughter was involved, as Ibn Battuta visited a few years later and found the city in fine shape.