I want to add a foreign key from Table Customers, row= \"Customer ID\" to Table Pet, row= \"Customer ID\".
-- Table struct
It looks like to me that you inserted values in table Pet's column ID when they should have been inserted in CustomerID and vice-versa.
By the way, it's not really good to have IDs as VARCHARs, specially when they are foreign keys. This makes queries processing slower, although your tables don't look like they'll have a huge number of rows for this to make a difference. Anyway, it's just an observation. I would consider have artificial int primary keys in my tables.
EDIT
I had misread table Pet's values. The other answers here are right. You need to update those 0 values in CustomerID column to match existing CustomerIDs in Customer table or delete them, otherwise you'll get an error when trying to create the FK.