Do I need to file a tax return working remotely in SC if our legal residence is in GA but we are renting a home in SC. I have not changed my physical address from GA?

You're a non-resident of SC for tax purposes.  Here is SC's definition of resident:

You are a South Carolina resident, even if you live outside South Carolina, when:

1. Y​our intention is to maintain South Carolina as your permanent home; AND
2. South Carolina is the center of your financial, social, and family life; AND
3. When you are away, South Carolina is the place to which you intend to return.

You are a nonresident if your permanent home is outside South Carolina all year and none of the above apply.​

The income you earn from working remotely in SC is taxable by SC.  Income earned from work carried on in SC is subject to SC taxation.

Since your domicile - your permanent home to which you intend to return  - is in GA, ALL your income is  taxable by GA, including your earnings from SC.

>>Therefore you must file both a non-resident tax return in SC and a resident tax return in GA.  You'll be able to take a credit on your GA return for the taxes paid to SC on the income taxed by both states, so you won't be double-taxed.

In TurboTax, be sure to complete the non-resident state tax return first, before your home state return, so that the credit is applied properly.