I have flown quite a lot with my pump.
Security (I think this is what you mean by TSA) is the only time anyone pays any attention to it.
The usual recommendation is that insulin pumps should not be x-rayed. This means you should keep it on (don't put it on the conveyor belt) and, as the other say, you are fine to go through the metal detector arch but generally not the full body scanner. Everywhere I have travelled in USA (Boston, Miami, Philadelphia, DC, ...), the security guys are familiar with the pump and what to do about it. Expect a bit of a wait whilst they find someone of your gender who is available to pat you down and then do as they ask you.
As for your doctor's letter, keep it somewhere you can get to easily. This could be in a pocket in your hand luggage (you won't be without it for long) or in your pocket (a piece of paper won't set off the metal detector).
Other things to think about on your trip
- if you are changing timezones, change the time on your pump whilst you are on the flight.
- work out what your backup plan is if your pump should fail. The chance of this happening is very small. But, it is better to be prepared beforehand when you can pack an alternative. This may be your basal bolus pens or a spare pump. Whichever you take, remember to make a note of your doses before you leave home.
- Many many many people travel with diabetes and with a pump so you are not alone.
- Have an amazing time