You might consider producing the table on the Part B sheet using Get & Transform (aka Power Query), although I'll imagine that someone will write you a FILTER function based formula before too long.
While not completely automatic it will only require that you select any cell in the green/white table > right click the mouse and select Refresh when any change is made to the table on the Part A sheet.
The Power Query Advanced Editor code to produce the green/white table is:
let
Source = Excel.CurrentWorkbook(){[Name="Table1"]}[Content],
#"Changed Type" = Table.TransformColumnTypes(Source,{{"First Name", type text}, {"Last Name", type text}, {"Start Date", type date}, {"Return to Work Date", type date}, {"Returned", type text}}),
#"Filtered Rows" = Table.SelectRows(#"Changed Type", each ([Returned] = "No"))
in
#"Filtered Rows"
Let us know if you have any questions.
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