We establish an isomorphism between the center End_Htw(1) of the twisted Heisenberg category of Cautis and Sussan and Γ, the subalgebra of the symmetric functions generated by odd power sums. We give a graphical description of Ivanov's factorial Schur P-functions as closed diagrams in H_tw and show that the curl generators of End_Htw(1) correspond to two sets of generators of Γ discovered by Petrov which encode data related to up/down transition functions on the Schur graph. Our results are a twisted analogue of those of Kvinge, Licata, and Mitchell, which related the center of Khovanov's Heisenberg category to the algebra of shifted symmetric functions.