You don't have to open Memento to use it. Capture something or ask a question without touching your phone.
Say “Hey Siri, capture in Memento” and dictate. It lands in your Inbox like anything else. Several phrasings work, so use whichever comes naturally: capture in, add to, remember in, save to, store in, put in, write down in, or jot down in Memento.
Say “Hey Siri, ask Memento” and ask your question out loud. Check Memento, search Memento, find in Memento, look in Memento, and what's in Memento work as well.
Note: If Siri opens Reminders instead, check that you don't have a Reminders list named after the app — Siri can't tell them apart.