Would it be easier for you to include a flag column in the source data such that you can simply filter out the unwanted data in Tableau?
Or else to include an update date / integer row id in your data so you can use incremental refresh?
That was an idea I'd had as well but what I need Tableau to do is to replace the data assigned to the most current week with my updated table. For example, let's say I ran the extract on Monday and it pulled in all data for the week of 1/13/2019 (just 2 days). If I ran the extract again today, I'd want to replace everything that was listed for the week of 1/13/2019 with my updated data, but retain all of the rows for the weeks previous.
If I add load date column or something of the like then Tableau would simply add the data from the most recent load dates, and would not delete what was already in the extract for the week of 1/13/2019. This would leave me with data duplication as I'd have one row of data for 1/13/2019 with a load date of 1/14 and another with a load date of 1/18.