In a two-Higgs-doublet model (2HDM), at the vicinity of the alignment limit, the extra contributions to the couplings of the SM-like Higgs with other particles can be subdominant to the same coming from the six dimensional operators. In this context, we revisit the alignment limit itself... It is investigated to what extent these operators can mask the actual alignment in a 2HDM. The bosonic operators which rescale the Higgs kinetic terms can lead to substantial change in the parameter space of the model. We find that some other bosonic operators, which are severely constrained from the electroweak precision tests, can also modify the parameter space of 2HDM due to their anomalous momentum structures. A particular kind of Little Higgs model is explored as an example of 2HDM effective field theory in connection with 2HDM alignment. Choosing a suitable benchmark point in a Type-II 2HDM, we highlight the possibility that the exact alignment limit is ruled out at 95% CL in presence of such operators. (read more)