If column C contains number only cells you can use a temporary helper column.
Sub x()
Dim rngData As Range
Set rngData = ActiveSheet.Range("A1").CurrentRegion
With rngData
.Offset(, .Columns.Count).Resize(, 1).FormulaR1C1 = "=ISNUMBER(RC[-1])"
End With
Set rngData = ActiveSheet.Range("A1").CurrentRegion
rngData.AutoFilter Field:=rngData.Columns.Count, Criteria1:="FALSE"
rngData.SpecialCells(xlCellTypeVisible).EntireRow.Delete
rngData.Columns(rngData.Columns.Count).Clear
End Sub
If this does not work you will need to post example workbook.
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