I'd echo Simon's comments.
Ignore, for now, any "moral" issues associated with failing to declare a result. I wouldn't lose too much sleep about that.
You can probably reach a decision based purely on a selfish risk/benefit analysis. The potential "benefit" in failing to declare the result is minimal - your overall academic results combined with place of study are easily sufficient to ensure that you're in the group of undergrads targeted by law firms. The 'C' grade will not make much difference.
On the other hand, the "risk" involved is substantial. If a firm was to discover your deliberate omission of a fact which might have played a role in their decision making process, then they will be less than impressed (even if the result in question would, in practice, have had a limited impact on their decision). In other words, the omission itself becomes more important than the grade. In those circumstances, you will be seen as someone who covers up something which needed to be explained - not a good look. Unfortunately, the "no-one will ever know" approach has a nasty way of failing with dramatic consequences. I "embellished" some parts of my application to Slaughters years ago and I got caught out. It was deeply embarrassing.
Include the result and, if you're still concerned, include some explanation in the usual "Anything else?" box on the application form.