Jamieson-Fausset-Brown on Numbers 31:48
officers . . . said . . . there lacketh not one man of us--A victory so signal, and the glory of which was untarnished by the loss of a single Israelitish soldier, was an astonishing miracle. So clearly betokening the direct interposition of Heaven, it might well awaken the liveliest feelings of grateful acknowledgment to God (Psa 44:2-3). The oblation they brought for the Lord "was partly an atonement" or reparation for their error (Num 31:14-16), for it could not possess any expiatory virtue, and partly a tribute of gratitude for the stupendous service rendered them. It consisted of the "spoil," which, being the acquisition of individual valor, was not divided like the "prey," or livestock…
Read the whole note in the consoleJohn Gill on Numbers 31:53
For the men of war had taken spoil, every man for himself. And which he kept for himself, and did not deliver in with the prey or booty, which was brought to Moses and Eleazar, the sum of which was taken by them; and this seems to confirm what has been hinted, that, as each soldier had taken spoil for himself, so everyone contributed his quota towards this freewill offering to the Lord.
John Calvin on Numbers 31:51–end
And Moses and Eleazar the priest took the gold. It was fitting that this should be added, lest any should suppose that Eleazar made a profit by the liberality of others. Moses, therefore, relates, that whatever gold was offered, was faithfully laid up as an ornament for the sanctuary. When it is said, "for a memorial for the children of Israel," it may be taken either actively or passively; viz., either that the gift may be a monument of their gratitude, or that it might conciliate favor for the people in the eyes of God; as if that offering of expiation brought before God, and represented, all those who thus professed themselves to be preserved by His grace. I prefer the latter sense myself…
Read the whole note in the consoleKeil & Delitzsch on Numbers 31:48–end