"Items" have a "retailers" field – here I call it "stores".

The Stores tiddler has a list field that lists the Stores. I'm also tagging them with Store.

!! List by retailer
<$list filter="[list[Retailers]]" variable="retailer">

!!! <<retailer>>
<$list filter="[<retailer>listed[retailers]tag[Item]]" variable="item">
<$checkbox tiddler=<<item>> tag="Selected"/> <$link to=<<item>>><<item>></$link><br/>
</$list>
</$list>

Grocery Item View Template

\define checkit() 
<$action-listops $field="retailers" $subfilter="[<retailer>]"/>
\end
\define uncheckit() 
<$action-listops $field="retailers" $subfilter="-[<retailer>]"/>
\end

\define allactions() <$action-deletefield dummy/>
<$list filter="[all[current]tag[Item]]">
''Retailers:''<br/>
<$list filter="[list[Retailers]]" variable="retailer">
<$list filter="[all[current]contains:retailers<retailer>]" variable="dummy">
<$checkbox field="dummy" checked="yes" unchecked="no" default="yes" uncheckactions=<<uncheckit>> actions=<<allactions>>/><<retailer>><br/> 
</$list>
<$list filter="[all[current]!contains:retailers<retailer>]" variable="dummy">
<$checkbox field="dummy" checked="yes" unchecked="no" default="no" checkactions=<<checkit>> actions=<<allactions>>/><<retailer>><br/> 
</$list>

</$list>
</$list>