Is it permissible for a woman to handle the semen of other men in her work at an IVF laboratory, given the availability of alternatives and the fact that it is more rewarding?

Semen itself is not considered 'awrah (private parts) that a woman is forbidden from seeing. Therefore, there is no objection to a wife working in the field of artificial insemination, provided it is free from unlawful prohibitions such as blameworthy mixing (of genders) and private seclusion with non-mahram men, while also observing the Sharia-compliant regulations regarding permissible and forbidden forms of artificial insemination.