Twisted Laguerre-Gaussian Schell model (TLGSM) beams are a novel type of partially coherent beams, which carry the twist phase and the vortex phase simultaneously. In this paper, the self-reconstruction (SR) of the TLGSM beam partially blocked by an opaque obstacle and propagating through a thin lens focusing system is studied in detail. Implementing the pseudo-mode expansion method, we represent the TLGSM beam as a superposition of spatially coherent modes, which is applicable for calculating the cross spectral density (CSD) and spectral degree of coherence (SDOC) of such a beam using the Fourier transform. The numerical results reveal that the twist parameter, a measure of the strength of a twist phase, determines the characteristics of the SR. In the case of the topological charge of the vortex is positive, the SR capability of spectral density is significantly improved with the increase of the twist parameter. The physical mechanism behind these phenomena is analyzed in detail from the point view of mode expansion. Further, the dependence of the side ring intensity and SR capability of the SDOC on the twist parameter are also investigated. It is found that the SR capability and side ring intensity of the SDOC are simultaneously enhanced for a large twist parameter, providing an efficient way to determine the number of topological charge. Our study results may find application in communication and information recovery applications.