It could probably be done more neatly with VBA code but I used VLOOKUP's.
I inserted a column to the right of every column you were interested in on the Needs Updating sheet, then named the data table (DataTable). The VLOOKUP for the first MTD number for example would be
=IF(ISERROR(VLOOKUP($A2,DataTable,3,FALSE)),"",VLOOKUP($A2,DataTable,3,FALSE))
Then if the new column is what you want, Copy and Paste Special >Values to remove the formulas and delete the extra columns.
I attached my example.
ChemistB
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