Is placing the hijab outside of work hours—due to work incompatibility—considered manipulation of religion, and what should be done about it?

It is permissible for a woman to work if the শরী‘আ (Islamic law) regulates are met. If there is a non-mahram man present at the workplace who can see you, then you are obliged to observe hijab. It is not permissible to remain with them if they do not allow it, except in cases of necessity (such as having no one to provide for you). Once the necessity ceases, the prohibition returns. However, if the work is restricted to women only, then there is no harm in removing the hijab.