Following is some code that should do the task for you:-
Application.DisplayAlerts = False
Dim val1 As Long: val1 = [F1]
Dim val2 As Long: val2 = [F2]
Dim lr As Long
lr = Range("I" & Rows.Count).End(xlUp).Row
Range("I1:I" & lr).AutoFilter 1, ">=" & val1, xlAnd, "<=" & val2
Range("I2:I" & lr).Delete
Application.DisplayAlerts = True
Following is the link to my test work book. Click on the run button to see it work:-
I have just used numbers as the values in the test work book.
The criteria values in F1 and F2 are also cleared ready for new values.
I hope that this helps.