Your options:
1. Restart the experiment with a new experiment key after your modification (no bias, but users may switch buckets and you throw away old data).
2. Do what you described (maybe carry over bias, users do not switch buckets, you throw away old data)
3. Make the modification and do not create a new phase (no carry over bias and no loss of old data, but the variation changing mid-experiment means your results combine two different types of features, the variation pre and post change)