Infrared back radiation is an energy accounting artifact used to confuse people. Net infrared radiation is the term of interest.
For those who want to learn the details of the earth’s energy budget I highly recommend this source:
http://oceanworld.tamu.edu/resources/ocng_textbook/chapter05/chapter05_06.htm
One needs to understand every jot of information in the figures above and why they are the way they are before presuming to be able to speak with any authority on the subject.