A friend of mine runs a coffee shop and has started making her own flavor syrups. Rather than having to carefully funnel syrup into old Torani bottles, she wanted to use wide-mouth canning jars - they're easier to fill, and they self-seal as the syrup cools. Then, when they're ready to be used, she can just replace the canning lid with this part, attach the pump, and it's ready to go.
I hacked this adapter together using the threads from kebes22's Syrup Pump Adapter (thing 403831) and coal160's Softsoap Pump Mason Jar Lid (thing 2129131) and, so far, it's worked great.
Note that this adapter only works with the threaded Torani / Davinci syrup pumps, and not with the black 1883 pumps.
I also created a version with its own threads to screw onto the jar, but I've been unable to print it successfully as the support material required tends to ruin the threads and leave a problematically rough inside surface of the lid.
I printed in PLA for ease and speed, but PETG is probably a better food safe option (you can do your own research on how food safe any 3D printing material is or isn't - there's a lot to read) if for no other reason than that it'll stand up to higher temperatures when you clean it. Printed at .1mm to minimize the amount of texture for food particles and bacteria to get caught in, and wet-sanded the bottom surface to makes sure it was perfectly smooth. Probably not necessary for home use, but these were made to be used in a commercial kitchen at a coffee shop, so I went above to appease the