Are you able to figure out what the character codes for both "≤" and "≥" in your database character set are? if so then maybe try replacing both characters in your query string with chrw(character_code).
I have just tested something along the lines of what you are trying to do using Excel as my database - and it looks to work fine.
Edit: assuming you are still stuck and looking for assistance here - could you confirm what database you are working with, and any type information setting for the "description" field you are looking to insert your string into?
Edit2: I am not familiar with SQL server, but isn't your "description" field set up to be of a certain data type? if so what is it and does it support unicode characters? ncharvar, nchar seem to be examples of sql server data types that support Unicode.
It sounds like you may also want to try and add an "N" prefix to the value in your query string - see
Do I have use the prefix N in the "insert into" statement for unicode? &
how to insert unicode text to SQL Server from query window
Edit3: varchar won't qualify for proper rendering of Unicode - see here What is the difference between varchar and nvarchar?. Can you switch to nvarchar? as mentionned above, you may also want to prefix the values in your query string with 'N' for full effect
Edit4: I can't speak much more about sqlserver, but what you are looking at here is how VBA displays the character, not at how it actually stores it in memory - which is the bottom line. VBA won't display "≤" properly since it doesn't support the Unicode character set. However, it may - and it does - store the binary representation correctly.
For any evidence of this, just try and paste back the character to another cell in Excel from VBA, and you will retrieve the original character - or look at the binary representation in VBA:
Sub test()
Dim s As String
Dim B() As Byte
'8804 is "≤" character in Excel character set
s = ChrW(8804)
'Assign memory representation of s to byte array B
B = s
'This loop prints "100" and "34", respectively the low and high bytes of s coding in memory
'representing binary value 0010 0010 0110 0100 ie 8804
For i = LBound(B) To UBound(B)
Debug.Print B(i)
Next i
'This prints "=" because VBA can not render character code 8804 properly
Debug.Print s
End Sub