Hey did this really work for you after all? I did what you said and was soooo excited thinking it was working as I was able to edit the price as you said and save it however my facebook shop still had the higher prices. super super annoying.. my email is email@example.com if you actually see this message
To solve this, I just toggled the visibility of the variant showed until the cheaper came up.
First I click the view on the website button to check the variant displayed (because I have some variant with the same price), then went to catalog on the facebook manager, select the product, select the variant, edit the product and toggle the visibility setting.
It is a shame that shopify doesn´t bother to offer a solution in 4 years. Even though this is a simple workaround, at least is not destructive (you don't need to eliminate product or recreate the product listing etc). It worked for me, If someone finds a better solution please share it
@karris7 I followed your advice and toggled the visibility and the cheaper price came up instead of the higher price, Yes!, thank you. However, when I checked back - this dearer item(s) has disappeared from my shop. Now, these variants have vanished in the Facebook catalogue>items, so if you want the variants back you need to create another listing inside the FB shop. I won't go there as I find it will go back to square one to show the higher price.
The only way around it is to keep one variant (lower price) and toggle the visibility for the rest of the variants in the FB catalogue - it will only display one variant (cheaper) in your FB shop and if you click the 'check out on website' button - your buyer can see all the rest of the variants in your own store.
I personally think the variants is a total waste of time to be in the Facebook shop, messes up the price option.