Sorry about your downgrade. Hope you enjoyed the TK J flight.

United policy is that if you flew any portion of your trip in the ticketed class of service (business), you are not owed a refund of the mileage cost from business back to coach.

Since it doesn't sound like anything went particularly wrong that was UA's fault to cause your misconnect, just bad luck on a short connection, I would not expect to get any mileage back. You should absolutely feel free to ask; can't hurt. You might question whether you were correctly placed on the waitlist for a J seat on your later IAH-LAX flight after you were reaccommodated; as a pax ticketed in J but with a Y seat assignment, you should have been eligible for a high-priority waitlist for a front cabin seat, and if they upgraded any other passengers ahead of you, that might be a problem, but it can be very hard for you to figure that out after the fact.