Very good point, but I personally say Itsuki was lying. This can't be proven or disproven definitely, but think about it this way...
An important thing to note is that at point in Chapter 34, Fuutarou has NOT brought up the topic of charms, even in the flashback. But for some reason, Itsuki was there to ask Fuutarou why is he studying so hard. And over the course of 33-34, we are given that...
-for a moment Fuu thought Itsuki as Lolikano (only Yotsuba has had the same privilege)
-Itsuki said the 'necessary' line that was NOT mentioned by (only Rena has the same privilege, maybe the intruder during "The moon is beautiful" chapter if you believe that was a Chekov's Gun)
-Itsuki brought a STUDYING charm... to a hospital? For what reason?
Not gonna lie, I thought I was overthinking things and maybe all of the above are red herrings. But when chapter 35 (I think?) came out with Fuu having a flashback with lolikano "setting an example" to her sisters, AND THEN in chapter 39, Itsuki encouraged Fuutarou to not give up with "Please don't start whining. You were going to set an example, weren't you?"
Not only that, but after all that transpires in chapter 39, Itsuki slapped Nino. Which in Nino's words in a later chapter as "something [Itsuki] would never have done in the past." So we know Itsuki wouldn't have sided with an outside over a family member, so there must be a special reason why, right? Is it possible that the reason why Itsuki did something "OOC" was because she was won over by Fuu "setting an example" to the quints, and she was won over by that BECAUSE she did the very same thing as a child?
At this point, which is the more likely scenario?
1) Itsuki not being Lolikano and was given the charms by someone esle
2) Itsuki being Lolikano, wanted to know if Fuu remembered the girl of the past WITHOUT revealing she is Lolikano, so she played dumb with the origin of the charm
I'd say it is the latter one, but everyone should make up their own minds.