I've noticed that Desdemona often claims that I haven't met Dr. Amari when sending me to her in this quest even if I have, so I opened up the quest in xEdit, and [INFO:00115A7A] ('You've dealt with her before. But you may not know of the vital role she plays in our organization.' in GRUP Topic Children of [DIAL:00115A63]) plays if MQ105 "Getting a Clue" [QUST:000229E6], stage 100 is complete. However, that quest stage is for noticing that Kellogg's Diamond City house is locked, so that I have to either pick the lock or get the key from the mayor. If I picked the lock ahead of time, it looks like stage 125 would be completed instead (with no journal entry). There is also the quest "The Memory Den" by which I could have met her.
Thus, there are several scenarios by which Desdemona will be wrong about whether I've met Dr. Amari:
1. I met her via "The Memory Den" quest, but haven't even rescued Nick Valentine yet. (she'll say I haven't met Dr. Amari)
2. I picked the lock on Kellogg's House ahead of time and talked to Dr. Amari after killing Kellogg. (she'll say I haven't met Dr. Amari)
3. I brought Nick to Kellogg's House and noticed it was locked, but paused doing main quest stuff sometime before actually going to Dr. Amari (possibly immediately, leaving Nick standing there outside Kellogg's house), and did Railroad quests. (I think she'll say I've dealt with Dr. Amari before, even though I haven't)
4. I went to the Memory Den, but I accepted Irma's statement about not accepting new clients, then walked further in and talked to Dr. Amari (at this point, neither "you haven't met her" nor "you've dealt with her before" would be entirely accurate)
#4 might be impractical to detect, but #1 could be checked by looking at whether FFGoodneighbor01 "The Memory Den" [QUST:00108EC0], stage 100 is complete. #2 and #3 could be handled better with a check for whether MQ202 "Dangerous Minds" [QUST:000229E9], stage 35 is complete - the note on this stage is "player steps into the lab".