You might need to update your published web service under the following two scenarios:
Your original model changed, for example, you modified the model parameters to improve performance and so on
You need to make changes to the input or output of the web service
For the first case, you need to go back to your original training experiment, make the changes, run it, and then click on the UPDATE SCORING EXPERIMENT link to update the scoring experiment. For both the scenarios, you have to go to the scoring experiment and publish it again, so it would overwrite the previously published experiment.