Thanks for the pix. Actually, I was hoping for some pix of the things inside of the jar and not the jar itself, but I can see why you wouldn't want to open it again. The jar's lid doesn't appear to be rusted. So maybe it hadn't been buried long?
Disclaimer: I'm not an expert on anything, so this is purely my opinion and personal suggestion, nothing more.
Was the jar dug up on private land with permission from the property owner? If yes, you had permission to dig on private land, then FIRST I would ask the landowner if he/she knew anything about the item inside the jar. If the person knows nothing about it, I would ask what they suggest and respect their opinion. Afterall, it was on their land. If, however, the private property owner did not give permssion to hunt on his/her land, I'd rebury the thing where I found it and forget the whole incident. No use getting into trouble digging without permission, which is what might happen if you did anything other than return the jar to the site.
Did you found it on public land which was OK to detect on? If this is the scenario under which you found the jar, I'd definitely report the find to local authorities. Here's why, no one should be burying any organic material on public property. There might be some disease/fungus/bugs that could be in the material. Finding syringes in public places is bad, but finding a fetus or a dead gerbil or any other potentially diseased dead thing is absolutely outrageous and needs to be reported so that the perpetrator can be apprehended. There are proper ways to deal with dead animals or fetuses, burying them illegally on public land is not acceptable. As long as you did nothing wrong in digging it up, you should have no problem reporting your find to the law enforcement agency with jurisdiction over the area in which the jar was found. You would be performing a public service if you reported it to the authorities so that they could properly dispose of the material in the jar. Whatever you do, don't touch the material in the jar and don't pour it out of the jar. It could be harmless or it could be opening Pandora's Box. Good luck, and please keep us informed as to the disposition of the jar.