expr[[First/@Position[expr,[CapitalDelta]]]]

expr = -Δ^2 - 3 ga^2 - gb^2 - Δ δa + δa^2 + Δ δb + δa δb + δb^2;
DeleteCases[_?(FreeQ[Δ])] @ Expand @ expr

expr2 = -(Δ^2 - 3 ga^2 - gb^2)^2 - Δ δa + δa^2 + Δ δb + δa δb + δb^2 ;
DeleteCases[ _?(FreeQ[Δ])] @ Expand @ expr2