On the basis of the 5ΛHe + N + N three-body model which has successfully been applied to a systematic study of the energy and nucleon halo structure of the A = 7 isotriplet hypernuclei, strengths of γ transitions in 7ΛLi and 7ΛHe are calculated. The new model confirms that the B(E2;5/2+→1/2+) value in 7ΛLi is reduced remarkably in comparison with the corresponding B(E2;3+→1+) in the core nucleus 6Li. This is due to the gluelike role of the Λ particle which induces a contraction of the core nuclear size. It is suggested that a measurement of the 5/2+→1/2+E2 transition rate in 7ΛLi (ongoing at KEK as E419) provides a unique opportunity to derive the hypernuclear size and hence to confirm the size contraction experimentally. The E2 and M1 transition strengths are also predicted for low-lying states in the hypernucleus 7ΛHe whose core nucleus 6He is known to have a neutron halo. Another prediction is made of much enhanced E2 transitions in 7ΛLi from the 5/2+ and 3/2+(T=1) states which are expected to have a proton halo structure.