I assume this happens when the Add Item button is clicked. I can see that you are creating a shopping item and setting its list to the parent’ group’s shopping list. I see you are also adding the new shopping item to the items list on the parent group’s grocery list. This all looks fine to me.
It’s difficult to understand the exact flow, without knowing what your app is trying to do, but I did notice that you have two groups called “Group Grocery List” and only one of them has a data source specified. Try naming them differently to avoid confusion and also try setting the outer one of the two to also have a data source of parent group’s grocery list - unless you’re dynamically setting it in a workflow (I couldn’t tell if you’re doing so or not).
If this doesn’t work, then I think you would need to explain here the flow of your app. I see a lot of references to inviter and invitee and their grocery lists but it’s not clear to me how it all works. With a bit more of an explanation, I, or others may be able to assist further.