Twist-3 Generalized Parton Distributions may provide an alternative source of information on quark orbital angular momentum. Additionally, twist-3 GPDs embody information on the spatial distribution of quark-gluon correlations. Spectator models are used to study general features that appear in twist-3 GPDs. We find in 1 loop calculations/spectator models that twist-3 generalized parton distributions exhibit discontinuities. In the forward limit these singular contributions grow into delta function contributions. These terms are essential for certain sum rules for twist 3 PDFs and neglecting these terms leads to an apparent violation of these sum rules. We identify these delta function terms with momentum components in the nucleon state that do not scale as the nucleon is boosted to infinite momentum.