Here are two possible workarounds:
1) Populate the field with incrementing values again using Field Calculator.
If you really need those values in ArcMap, go to field calculator and enter the following code block (taken from the ArcGIS Calculate Field Examples), making sure you specify Python as the parser:
pStart = 1 #adjust start value, if req'd
pInterval = 1 #adjust interval value, if req'd
if (rec == 0):
rec = pStart
rec = rec + pInterval
In the expression you should write:
2) Delete the Ref column from the spreadsheet. If the resulting table in ArcMap contains a FID field, you would not need the Ref column as it contains the exact same values.