When my restaurant server comped my entree, with the only reason being "I took care of it", should I tell the manager or let it go?

Generally speaking, since orders are recorded in the kitchen AND the server's ticket, they can't comp anything without the manager's approval.

If it was actually comped, the manager already knows about it.

Take the win and go with it! Chances are a supervisor had to comp the check themselves and they already know. If not, your server is stealing and their employer is already on to them. Restaurants don't give away things without reason, and with profits and losses accumulating from a multitude of sources guest checks are monitored closely. POS systems track everything. How many burgers were ordered, how many desserts were made, how many discounts were applied, and even when one of us screws up making a drink or forgetting to modify the meal per customer request. Also they track any food that has expired and was thrown out. Trust your server did the right thing. Dont question it. 

By all means, tell the manager, get this guy in trouble, who was just trying to do you a favor. (sarcasm)

I would just let it go,but if it really bothers you, then you should go ( or should have gone) and talk to ( or talked to, in this case, since it's been at least 5 hours) to the manager about it.

Why would you tell the manager??? I don't really understand your question. Are you trying to get the server in trouble for giving you a discount? That just seems rude. Are you trying to protect corporate profits? That just seems weird.

Seriously, what is going through your head to think you should report this? Were you a hall monitor in middle school?

You should say "thank you" and let it go at that.