Since you want to use the left button to select the items, I assume you don't want Item Click behaviour? In that case, use the following...
<GridView
ItemsSource="{Binding Source={StaticResource groupedItemsViewSource}}"
ItemTemplate="{StaticResource Standard250x250ItemTemplate}"
SelectionMode="Multiple"
IsSwipeEnabled="false"
IsItemClickEnabled="False" />
If you want to allow the item click behaviour, you would set IsItemClickEnabled = true;
and use the built-in swipe selection mechanism for selecting items.
<GridView
ItemsSource="{Binding Source={StaticResource groupedItemsViewSource}}"
ItemTemplate="{StaticResource Standard250x250ItemTemplate}"
SelectionMode="Multiple"
IsSwipeEnabled="true"
IsItemClickEnabled="true"
ItemClick="ItemView_ItemClick">