The results for LDA look strange, and actually the LDA basis set for Te looks wrong too (you can inspect it in VNL 11.2 by choosing Analyzer>Basis Set Explorer). There are 2 valence states (5s,5p), but if we check the DoubleZeta basis set, for GGA it looks normal, but in LDA we have 3 functions with nodes at r=0. If you zoom in, however, one of them is actually finite at r=0, but much too small. Also, the s state seems completely linear for small r.
Since the GGA results seem reasonable, you should definitely use GGA for this system.