The phrase "letting in" can be replaced with a variety of synonyms depending on the context. Some possible options include welcoming, admitting, permitting, allowing, enabling, authorizing, sanctioning, and endorsing. These words all imply some form of giving permission or access to something or someone. For example, you might use "welcoming" to convey a friendly reception of a person into a group, or "permitting" to describe granting access to a particular location or resource. "Authorizing" and "sanctioning" may be more appropriate in more formal or regulated situations, such as approval of a legal document or compliance with a policy. Ultimately, the best synonym for "letting in" will depend on the specifics of the situation and the tone of the language being used.