The maintenance schedule for your specific vehicle can be found in the Owner's Manual- just thought I'd mention it so you'll know it's there if you need it in the future.
The Acura maintenance schedule indicates that the timing belt needs to be changed at 105,000 miles OR 7-years (whichever comes first)! Your 2003 TL has very low mileage for the year model- roughly 8500 miles year aveage. The maintenance schedules for your car are calculated at a much more common rate of 15,000 miles per year.
While you have far less than 105,000 miles on your car, it has been in service for seven years. Timing belts are made of rubber, so they will deteriorate over time regardless of mileage. So technically, your car is DUE for a timing belt replacement based on age!
It's very possible that your 60k/7yr old timing belt could be fine for another 20-30k miles. But the consequences of a timing belt failure are HUGE and the risk simply isn't worth putting it off! If the timing belt fails on an "interference" engine, the open valves will stick open and make contact with the pistons (translation- All Hell Breaks Loose) and the engine is destroyed!!!
On most Honda models, including your TL, the water pump is driven by the timing belt. Since the timing belt replacement is a labor-intensive job (4-5hrs of labor), it's highly advisable to replace the water pump simultaneously. A lot of mechanics even refer to it as a "timing belt and water pump replacement" because they always do both while they're in there. In my experience with various Hondas from the late 80s to present, the water pumps are only designed to last between timing belt replacements! So if your water pump failed before you replace your timing belt, you would be replacing it then. That's why I would go ahead and circumvent any potential problems, both minor and catastrophic, by replacing the timing belt and water pump now. =)