sqlservercentral.com[
^] has some useful snippets for dates.
Try something like (caveat - untested)
SELECT *
FROM objectives
WHERE CompetionDate >= dateadd(wk, datediff(wk, 0, getdate()), 0)
AND CompetionDate < dateadd(wk, datediff(wk, 0, getdate()) + 1, 0)
AND Comp_Id=161
If your week doesn't start on a Monday then change the 0s to the appropriate number.