If you will never physically work within VT, then you will have no income tax liability to the State of Vermont.
A handful of states tax non-resident remote workers; Vermont is not one of them. Your income will be 100% taxable by your home state of SC.
As @awillis2 said, if your employer will not withhold SC taxes for you, then you must make quarterly estimated tax payments to SC.
If you will never physically work within VT, then there is no need for your employer to withhold VT taxes from your pay.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
