I looked at this as not getting rid of 'spaces' but being left with only decimal characters. This code did that for me:
phoneNumberString = [[phoneNumberString componentsSeparatedByCharactersInSet:[[NSCharacterSet decimalDigitCharacterSet] invertedSet]] componentsJoinedByString:@""];
This takes out everything that's not a number 0-9.
Swift 4.1:
phoneNumberString = phoneNumberString.components(separatedBy: CharacterSet.decimalDigits.inverted).joined(separator: "")