For .docx (Open Xml) files, the most simple way is to use the official Open XML SDK nuget package. With this, it's very easy to manipulate document properties:

// open for read write
using (var package = WordprocessingDocument.Open("myfile.docx", true))
{
    // modify properties
    package.PackageProperties.Creator = null;
    package.PackageProperties.LastModifiedBy = null;
    package.PackageProperties.Revision = null;
}

For .doc (Word .97->2003) files, here is a small C# method that will be able to remove the properties (which are technically stored completely differently):

RemoveProperties("myfile.doc", SummaryInformationFormatId, PIDSI_AUTHOR, PIDSI_REVNUMBER, PIDSI_LASTAUTHOR);

...

public static void RemoveProperties(string filePath, Guid propertySet, params int[] ids)
{
    if (filePath == null)
        throw new ArgumentNullException(nameof(filePath));

    if (ids == null || ids.Length == 0)
        return;

    int hr = StgOpenStorageEx(filePath, STGM.STGM_DIRECT_SWMR | STGM.STGM_READWRITE | STGM.STGM_SHARE_DENY_WRITE, STGFMT.STGFMT_ANY, 0, IntPtr.Zero, IntPtr.Zero, typeof(IPropertySetStorage).GUID, out IPropertySetStorage setStorage);
    if (hr != 0)
        throw new Win32Exception(hr);

    try
    {
        hr = setStorage.Open(propertySet, STGM.STGM_READWRITE | STGM.STGM_SHARE_EXCLUSIVE, out IPropertyStorage storage);
        if (hr != 0)
        {
            const int STG_E_FILENOTFOUND = unchecked((int)0x80030002);
            if (hr == STG_E_FILENOTFOUND)
                return;

            throw new Win32Exception(hr);
        }

        var props = new List<PROPSPEC>();
        foreach (int id in ids)
        {
            var prop = new PROPSPEC();
            prop.ulKind = PRSPEC.PRSPEC_PROPID;
            prop.union.propid = id;
            props.Add(prop);
        }
        storage.DeleteMultiple(props.Count, props.ToArray());
        storage.Commit(0);
    }
    finally
    {
        Marshal.ReleaseComObject(setStorage);
    }
}

// "The Summary Information Property Set"
// https://msdn.microsoft.com/en-us/library/windows/desktop/aa380376.aspx
public static readonly Guid SummaryInformationFormatId = new Guid("F29F85E0-4FF9-1068-AB91-08002B27B3D9");
public const int PIDSI_AUTHOR = 4;
public const int PIDSI_LASTAUTHOR = 8;
public const int PIDSI_REVNUMBER = 9;

[Flags]
private enum STGM
{
    STGM_READ = 0x00000000,
    STGM_READWRITE = 0x00000002,
    STGM_SHARE_DENY_NONE = 0x00000040,
    STGM_SHARE_DENY_WRITE = 0x00000020,
    STGM_SHARE_EXCLUSIVE = 0x00000010,
    STGM_DIRECT_SWMR = 0x00400000
}

private enum STGFMT
{
    STGFMT_STORAGE = 0,
    STGFMT_FILE = 3,
    STGFMT_ANY = 4,
    STGFMT_DOCFILE = 5
}

[StructLayout(LayoutKind.Sequential)]
private struct PROPSPEC
{
    public PRSPEC ulKind;
    public PROPSPECunion union;
}

[StructLayout(LayoutKind.Explicit)]
private struct PROPSPECunion
{
    [FieldOffset(0)]
    public int propid;
    [FieldOffset(0)]
    public IntPtr lpwstr;
}

private enum PRSPEC
{
    PRSPEC_LPWSTR = 0,
    PRSPEC_PROPID = 1
}

[DllImport("ole32.dll")]
private static extern int StgOpenStorageEx([MarshalAs(UnmanagedType.LPWStr)] string pwcsName, STGM grfMode, STGFMT stgfmt, int grfAttrs, IntPtr pStgOptions, IntPtr reserved2, [MarshalAs(UnmanagedType.LPStruct)] Guid riid, out IPropertySetStorage ppObjectOpen);

[Guid("0000013A-0000-0000-C000-000000000046"), InterfaceTypeAttribute(ComInterfaceType.InterfaceIsIUnknown)]
private interface IPropertySetStorage
{
    void Unused1();
    [PreserveSig]
    int Open([MarshalAs(UnmanagedType.LPStruct)] Guid rfmtid, STGM grfMode, out IPropertyStorage storage);
}

[Guid("00000138-0000-0000-C000-000000000046"), InterfaceTypeAttribute(ComInterfaceType.InterfaceIsIUnknown)]
private interface IPropertyStorage
{
    void Unused1();
    void Unused2();
    void DeleteMultiple(int cpspec, [MarshalAs(UnmanagedType.LPArray, SizeParamIndex = 0)] PROPSPEC[] rgpspec);
    void Unused4();
    void Unused5();
    void Unused6();
    void Commit(uint grfCommitFlags);
    // rest ommited
}