Navigate to Feed Rules in the feed tool. To begin, select Identifier Exists as your attribute to Modify:

Filtering 

NOTE: Generally speaking, if you did not include GTINs for products in your store then you can apply a filter for the following (continue reading for general filter building guidance):

Field > GTIN   Type > Is Empty  (No value needed)

Build filters to ensure your modifications are only applied to products that match your criteria. By not creating a filter, you are enabling a rule to apply to ALL PRODUCTS in your feed. Filters can consist of single attribute criteria or multi-attribute criteria by clicking Add Filter to build each additional criteria desired.

Filters can differ by their function using AND / OR logic. To create an OR logic, a filter must have multiple values entered at once:

To create AND logic, there must be multiple filters that all determine the select criteria:

Nullifying Brand & MPN

Repeat the steps above, adding rules for both Brand & MPN and setting the Text Attribute Builder to [Null]:

Set the same Filters from your Identifier Exists Rule, click Save once complete.

You can now send your feed to update it in Merchant Center.