I'd throw them out.

It ensures the jars are heated so they do not expand and crack when filled with hot items.

I heat my jars using the sterilize cycle in my dishwasher because it would be unsafe for me to move hot jars, with water, without lids, in and out of my canner due to the height of it on the stove. My dishwasher is certified for sterilization of food surfaces. I have also heated freshly dishwasher sterilized in the oven. However, sterilization is often unnecessary, and freshly clean jars are suitable for some canning processes. I do it anyway, just as an extra step in food safety. New regulations have come out since my All American canning manual was written, and regulations have changed for canning times and processes about sterilization. Here is a recent excerpt from Clemson Cooperative Extension. Is it necessary to sterilize jars before canning? Jars do not need to be sterilized before canning if they will be filled with food and processed in a boiling water bath canner for 10 minutes or more, or if they will be processed in a pressure canner. Jars that will be processed in a boiling water bath canner for less than 10 minutes, once filled, need to be sterilized first by boiling them in hot water for 10 minutes before filling them.

It is painful, but congratulations on stepping up your kitchen food safety! I have made errors in the past with egg storage and egg gathering, so this is what I would do. For me (and you should make your own decision), it would depend on how long the eggs were in the hydrated lime solution. If it has only been a few days or up to two weeks, I would use them for animal consumption, but they should not be stored raw in the fridge. They need to be cooked to stop any further food-borne microorganisms from growing. Because they were not washed, there is a high risk of botulism contamination as only a few microorganisms can proliferate in the microscopic crevices of the pickling lime particles. Boiling the eggs in a solution of water and vinegar can help remove microorganisms by heat and acid from the shell. After being cooked, they should keep for a few days in the fridge. Mark them well or store them in a ziplock bag so they can not be mistaken for human consumption. The eggs may have a high calcium content, so I would only use them for poultry or pigs. Smash them with a potato masher and feed them back to your poultry over the next few days. This way, you get your hard-earned eggs back in meat (if you raise meat birds) and more eggs. If Feeding them to pigs, only provide a few at a time as excessive egg shells can impact their colon and harm the gut lining. If you want to feed them to your dogs, I would crack them open, scramble them and place them into a well-greased casserole dish or roasting pan, cover them, and bake at 350F until well done. When cool, cut into serving sizes or snack sizes. Set a few servings aside that can keep in the fridge for a day or two, and place the rest on a cookie sheet to freeze. Freeze for 24 hours and toss into a ziplock bag. Your dogs might love these frozen snacks! Add the shells to your garden, compost pile, or crush them to give back to your poultry as a calcium supplement. This is a great question. Thank you for asking. Here is to your advancement in your health and a happy pantry! - Adrienne

I buy them at Walmart. You can use any container that will fit your vacuum bags. Polyethylene is the safer of plastics to use.