Here is how you can re-write the ClaimItemStatus function to be inline table-valued

create function dbo.ClaimItemStatus
( 
   @ClaimItemPk int,
    @Start Date,
    @End Date,
    @DayLimit Int
) 
RETURNS TABLE
AS 

with cte as (select case when @Start IS NOT NULL and @End IS NOT NULL 
          THEN 'Settled'
         WHEN @Start IS NOT NULL 
                  case when @DayLimit > (select count(*) .... ) -- here we can either use direct query or your scalar function - I prefer direct count
                      THEN 'OverDue'
                  else
                       'Pending' 
               END
        ELSE -- what else is not covered ?
           'Unknown'
      END as StatusDescr)

select StatusDescr, case StatusDescr WHEN 'Settled' then 2 when 'Pending' then 4 when 'OverDue' then 3 when 'Unknown' then 5 end as [Status]
from cte

GO

You can re-write your other functions in a similar way to become inline table-valued functions.

Note, that you will not be able to re-write them using the same name without dropping them first. For now you can use different names for these functions.

To test for now

select * from dbo.ClaimItemStatus(1, '20100101','20110101',5)

--Or

select CI.*, S.*
from ClaimItems CI
CROSS APPLY dbo.ClaimItemStatus(CI.ClaimID, CI.ClaimStartDate, CI.ClaimEndDate, CI.ClaimDayLimit) S

----------------


Your original:

BEGIN
	DECLARE @Status INT
	DECLARE @LapsedDays INT
    SET @Status = 1

    /* if no date forwarded then Pending */
    IF NOT @Start IS NULL
    
		/* if end date present, then Settled */
		IF NOT @End IS NULL
			SET @Status = 2 /* Settled */
		ELSE
			/* otherwise check if exceeded company limit of days lapsed */
			BEGIN
				SET @LapsedDays = dbo.GetWorkingDays(@Start, GETDATE())
				IF @LapsedDays > @DayLimit
					SET @Status = 3
			END

    RETURN @Status 
END