Remove one smaller database from larger, master customer database

You could use something like this.

Assuming that big list is in sheet1! column A starting in A2 and the small list in sheet2 starting in A2.

So in B2 of sheet1 put this and copy down as you need.

Formula:

=COUNTIF(Sheet2!$A$2:$A$600,A2)>0

Filter by TRUE in column B and delete all these records.