I am curious: in the Old Testament, what was done with the piece of foreskin that is a type of putting off of the sins of the flesh (Colossians 2:11) by the circumcision of Christ? We know that Jesus was the sin offering acceptable to God and as such his body of flesh is being burned outside the camp (Hebrews 13:10-13). It would not surprise me if those foreskins that were cut off by the Levite priest were also burned on the altar where the sin sacrifices were burned.
"We have an altar from which those who serve the tabernacle have no right to eat. For the bodies of those animals, whose blood is brought into the sanctuary by the high priest for sin, are burned outside the camp. Therefore Jesus also, that He might sanctify the people with His own blood, suffered outside the gate. Therefore let us go forth to Him, outside the camp, bearing His reproach" (Hebrews 13:10-13).
The writer of Hebrews did not say that Jesus' body is continually being burned outside the camp. He is drawing a parallel. Sin offerings were not offered on the regular altar but were burned outside the camp of Israel (Leviticus 4:11-12, 21). Since Jesus' sacrifice was for sin, it was fitting that his death also took place outside the city of Jerusalem. Thus the author is inviting the Jews to leave the Jewish religion (go outside the camp) to join with the Savior. "In that He says, "A new covenant," He has made the first obsolete. Now what is becoming obsolete and growing old is ready to vanish away" (Hebrews 8:13). The Jews were trying to hold on to their old religion and the writer is telling them that it is time to let it go.
In regards to the foreskins, nothing is stated about the disposal, but since trash was typically burned outside the camp, that was likely what was done with such things. "But the flesh of the bull, with its skin and its offal, you shall burn with fire outside the camp. It is a sin offering" (Exodus 29:14). However, since we aren't told, it would be improper to build ideas upon guesses.