You don't need the table declaration section. The function itself is a table variable. Your function needs only to have the SELECT statement in it.

CREATE function new_function (@some_param nvarchar(20)='MISSED')

RETURNS TABLE

AS

RETURN(

select MAX (LEGAL_NM) AS LEGAL_NAME,

MAX (TCPRL.VEND_CO_ID) AS VEND_CO_ID,

MAX(tcx.max_process_date) as LTST_PROCESSED_CHK_DATE

FROM t_bps_company_extract TCX

INNER JOIN T_COMPANY_PAYROLL TCPRL

ON TCPRL.Vend_CO_ID=TCX.VEND_CO_ID_TEXT

WHERE TCX.Company_status = 'Active'

group by TCPRL.vend_co_id, TCX.LEGAL_NM

)

GO