what columns to include in the index to improve the performance of the following update? I have the following update:

  UPDATE dbo.fees  
  SET amount = @amount,  
   currencyCode = @currencyCode,  
   feeType = @feeType,  
   countryCode = @countryCode,  
   gatewayCode = @gatewayCode,  
   programAP = @programAP,  
   programED = @programED,  
   programEX = @programEX,  
   mandatory = @mandatory  
  WHERE feeID = @feeID  and endDate = @endDate   
  and programAP = @programAP and programED = @programED and programEX = @programEX  
  and (countryCode = @countryCode or countryCode IS NULL)  
   and (gatewayCode = @gatewayCode or gatewayCode IS NULL)  


this is the table definition:

CREATE TABLE [dbo].[fees] ( 
[ID]            INT              IDENTITY(1,1)   NOT NULL,
[feeID]         INT                              NOT NULL,
[startDate]     DATETIME                         NOT NULL,
[endDate]       DATETIME                             NULL,
[amount]        DECIMAL(10,2)                        NULL,
[currencyCode]  CHAR(3)                              NULL,
[feeType]       CHAR(1)                              NULL,
[countryCode]   CHAR(2)                              NULL,
[gatewayCode]   CHAR(3)                              NULL,
[programAP]     BIT                                  NULL,
[programEX]     BIT                                  NULL,
[programED]     BIT                                  NULL,
[mandatory]     BIT                                  NULL  CONSTRAINT [DF_fees_mandatory] DEFAULT ((0)),
CONSTRAINT   [PK_fees]  PRIMARY KEY CLUSTERED    ([ID] asc) WITH FILLFACTOR = 90)


this is the index I intend to create in order to improve the performance of the update.

create nonclustered index i_feed2 on dbo.fees  (feeID ,programAP,programED,programEX,endDate) include (countryCode,gatewayCode )
with(data_compression=page,online=on) on [NONCLUSTERED_INDEXES]


A question came to my mind though:
what sort of data analysis should I do, to identify which of these columns would be better in the index or in the include part? Plus, the order of the columns in the index, is there any starting point as to find out, for this query in particular, or other queries that might hit this table, the best order of the columns?

There are no other indexes on this table.

I cannot change neither the table definition nor the update statement, but I can add indexes.

the solution 

On this occasion though, even after adding the index as planned, while monitoring the execution and using the very helpful procedure sp_blitzcache
that I contacted the third party company requesting them to alter the procedure accordingly (adding a with recompile and sort out the updates as described in the comments and the accepted answer)

sp_blitzcache in action:
I fail to see how included columns can be anything but overhead for an UPDATE. If you think about it... Included columns are there to eliminate the lookup for each row. But you still have to get to the row (do the lookup) in order to modify it for an update. And every time a column is in an index (included or key) this value have to be updated (in addition to the actual data) when a modification occurs.