North American Regulations on 433MHz Radio
I have a similiar device, and just wanted to clarify something:

For a low power 433MHz transmitter, those would fall under under the provisions of FCC Part 15.231 for periodic transmission (which permits operations at 433MHz).

The RFID container thing in FCC Part 15.240, that's for more of a continuous transmit scenario (at I believe higher transmit limits).

Operating conditions are quite different under those two rule parts. 

It is confusing and when you look at FCC Part 15.240, you might think you cannot use 433MHz for your typical low power transmitter, but that is not the case.

You can do a search on the FCC grantee database, and see TONS of transmitters at 433MHz. 

You just can't run a high power, continuously transmitting device using 433MHz.  

Your 433MHz transmitter has to fall under the rules for Part 15.231.