How to remove unknown zero-width character from string?

You can see the zero-width character using FullForm:

str //FullForm

"\:200b\:200b4-6"

So, in this case, you can use the following:

StringReplace[str, "​\:200b"->""] //FullForm

"4-6"

Update

Added a threshold, default 2, for determining "zero" width characters

You can use the following function to look for zero-width characters in your string:

findZeroWidthCharacters[str_, threshold_:2] := With[
    {chars = DeleteDuplicates[Characters[str]]},

    Cases[
        Rasterize[
            Row @ MapThread[
                Tooltip,
                {chars, ToCharacterCode[StringJoin@chars]}
            ],
            "Regions"
        ],
        Rule[{code_, _}, {{l_, _}, {r_, _}}] /; r-l<=threshold :> code
    ]
]

Here I apply it to your string:

findZeroWidthCharacters[str]

{8203}

Here I apply it to a longer string:

s = ExampleData[{"Text", "AliceInWonderland"}] <> FromCharacterCode[{8203, 8204, 8207}];
StringLength[s]

findZeroWidthCharacters[s] //AbsoluteTiming

51725

{0.170908, {8203, 8204, 8207}}

how about:

ascii = StringJoin@ FromCharacterCode[Range[0, 127]]; 
 StringReplace[str, c_ /; StringFreeQ[ascii, c] -> ""]
Head /@ ToExpression/@StringSplit[%, "-"]

{Integer, Integer}

or even FromCharacterCode[Select[ToCharacterCode[str], # <= 127 &]]

You might even extend that range if you have printable non-ascii characters. In your example the offending character is # 8203

Following a similar logic to george2079:

StringReplace[ImportString[ExportString[str,"Text", CharacterEncoding->"ASCII"]],
"\\:"~~Repeated[HexadecimalCharacter,4]->""]