Yeah, if you were Microsoft, would you want to hand someone that kind of authority over a SQL Server?   Think about how easy it would then be to take over...

In this case, it appears that your expression already includes a function in it:  TimeLineMatch.   Not sure how that affects things or what kind of function it is.   I personally...

Lynn's code, formatted for readability and avoids the significant repetition:
USE msdb
GO

CREATE PROCEDURE dbo.sp_getbackuphistory
    @DATABASE varchar(50),
    @TimeDiff int OUTPUT,
    @LatestBackupFinishDate datetime OUTPUT
AS
BEGIN
    SELECT
        @LatestBackupFinishDate...

I get the feeling that the problem is not enough NULL handling.   Try the following:
CREATE PROCEDURE [dbo].[usp_test]
@year char(4),
@criteria varchar(50) = NULL,
...