How to suppress sites from shop picker?

I have a multisite install with FrameMarket and MarketPress installed.

However some of the sites will only use global shortcodes to pull products into the site context. These sites have the “Buy Now” button that takes the visitor to the other site that has the cart for that product.

The problem I am seeing is that the Shop Picker appears to be displaying ALL the sites – not just the ones with stores.

I am not sure if it is relevant, but I do have FrameMarket and MarketPress enabled as Network Plugins.

Is there a way to suppress sites from showing up in the shop picker?