What is the method to determine the XOR placing in CRC code with random generator
You can see the generic case (CRC-n) as:


Here, when \$a_k=0\$, the AND gate where it is connected to, results in 0, what makes the XOR gate a pass thru. When \$a_k=1\$, the AND gate connects the feedback loop to the XOR gate, as expected.

Now, for your particular case, \$n=3\$, and CRC-3 defined as \$X^3+X^1+1\$ you have:


What is equivalent to: