Type IIB string theory on AdS₃ × S³× T⁴ with RR flux as the near-horizon limit of the D1-D5 solution is expected to be dual to a (4,4) supersymmetric 2d CFT parametrized by the integers Q₁,Q₅ and other moduli. It is related by T-duality to type IIA string theory in the near-horizon limit of the D2-D4 solution which admits an uplift to the 11d AdS₃ × S³× T⁵ background which is the near-horizon limit of the M2-M5 solution. We point out that this relation allows one to use the quantum M2-brane description to probe ``non-planar'' corrections in the dual 2d CFT, in close analogy with the ABJM theory case (described by M-theory on AdS₄ × S⁷/Zₖ). We consider an analog of a supersymmetric Wilson loop (line defect) expectation value represented by type IIA string partition function expanded around AdS₂⊂ AdS₃ minimal surface. Its M-theory analog is the M2 brane partition function expanded near AdS₂× S¹. We compute the 1-loop contribution Z₁ to the M2 brane partition function and find that in contrast to the ABJM case in arXiv:2303.15207 (where Z₁= (2sin2π/( k))⁻¹ = k/( 4 π) +π/( 6k) +... contains an infinite series of higher genera string corrections, k⁻¹ ∼ gₛ/( √(rm T))), here it is given solely by the leading string-theory contribution Z₁= κ/( √2π) where κ ∼ √Q₅ plays a role analogous to k. We also discuss a generalization to the mixed flux case which is straightforward from the 11d perspective.