The first sentence has a "do" in its subject, which allows a bare infinitive in the complement. The second sentence does not. When the subject (before was) already has a form of "do" (had to do), the verb after was is often the bare form (send). The "do" carries the carries an action, so you don't need another "to." You can still add it to be more formal/complete. In the sentence "Their goal was to influence everyone," the subject is the abstract noun "goal." When the subject is a noun for an idea, plan, or goal, you need "to" to introduce the action that defines it. The "to" connects the idea to its purpose. It answers the question "What was the goal?" -> "To influence everyone."

i don't know if this is 'officially correct' but my impression is that you don't need it TO is in the clause right before it, so it's kind of implied.