Thick ideals in Deligne's category Re_p(Oδ)

We describe indecomposable objects in Deligne's category Re_p(Oδ) and explain how to decompose their tensor products. We then classify thick ideals in Re_p(Oδ). As an application we classify the indecomposable summands of tensor powers of the standard representation of the orthosymplectic supergroup up to isomorphism.