The network of cosmic strings generated in a phase transition during inflation enters the scaling regime later than that of usual strings. If it occurs after the recombination, temperature anisotropies of the cosmic microwave background (CMB) at high multipole moments are significantly reduced. In this paper, we study such effects qualitatively and show that the constraint on the cosmic string tension from the CMB temperature anisotropies and B-mode polarizations can be relaxed. It is shown to be difficult to explain the recent BICEP2 and POLARBEAR results in terms of signals induced by cosmic strings alone even if we take into account the delayed scaling. However, the inflationary tensor-to-scalar ratio required to explain the observed B-mode signals can be slightly reduced to be consistent with the Planck constraint.