Absolutely refreeze the bones.
As long as food is kept at refrigerator temperatures, there is no danger to refreezing. One thing that will happen is some damage to the meat. Freezing makes ice crystals from the moisture in the meat. As ice crystals form, they damage cells. If you thaw and refreeze, you are creating new ice crystals that will also damage cells. If enough of this happens, the meat's texture can change enough to be noticeable.
If the meat never gets warmer than refrigerator temps, there is no food safety issue.
"If you want to make an apple pie from scratch, you must first create the universe." -Carl Sagan