This is exactly why you use setters rather than exposing the objects fields to the whole wide world.
Consider a class that holds an integer angle that's expected to be between 0 and 359 inclusive.
If you expose the field, calling functions can set it to whatever they want and this would break the contract specified by your API. It's also likely to break your functionality somewhere down the track because your code is written to assume a certain range for that variable.
With a setter, there's a number of things you can do. One is to raise an exception to indicate an invalid value was passed but that would be incorrect in my view (for this case). It's likely to be more useful if you modify the input value to something between 0 and 359 such as with:
actualVal = passedValue % 360;
As long as this is specified in your interface (API), it's perfectly valid. In fact, even if you don't specify it, you're still free to do whatever you want since the caller has violated the contract (by passing a value outside of range). I tend to follow the rule of "sanitize your input as soon as possible".
In your specific case, as long as you specify that the string is stored in trimmed format, there's no reason for callers to complain (you've already stated that such a string is invalid). It's better in terms of code size (not speed) to do it in the setter rather than at every piece of code that calls the setter. It also guarantees that the string is stored as you expect it to be - there's no guarantee a caller won't accidentally (or purposefully) store a non-trimmed string.