[edited at oct 16, applying errata]

This card's effect is quick strong; Amanda cannot use a skill card during one round, and her net stat is reduced by 1 (from errata, commiting card is not optional but mandatory Forced one).

However, this weakness does not have any terrible panelty like other weakness skill such as returning if failed or commiting only your test. Thus, to avoid significant penalty, you just commit this card at ANY test before start of investigate phase. -1 skill value for one test is neglectable effect.

Here are several ideas:

• Search your deck and/or draw many cards: If you draw this card during your turn, it's ok you just commit this. Mr. "Rook" is suitable for this. You can search 9 cards, and draw this for free. (But 4xp with taboo)
• Commit during mythos phase: If you draw this card during upkeep phase, only chance is mythos phase. It may be a better choice that you commit this at encounter test. If a encounter doesn't have any test, you may want to find a test for this. Some cards make you initiate a test at any window: Cipher's ability, or Expose Weakness (if a enemy in your location). You have a window just before the end of mythos phase.
• Keep her signature and replace: Obscure Studies can be an emergency button. If this weakness exists beneath Amanda, play her signature and commit (returned) this weakness.

Taboo version of Scroll of Secrets can be another solution. You may trigger that ablitiy during upkeep phase window, and you can place 2 of those card on top of your deck and those card is drawn at upkeep phase & beginning of investigation phase.

Not much of a weakness, to be honest, although at least it messes with Amanda's mechanics. Looking at the two elements, the effect and the discard condition, we get:

The effect: If this is in Amanda's hand at the beginning of the Investigator Phase, she must put it underneath her, making her a poorer Preston. elkeinkrad's suggestions of how to deal with it are pretty solid -- commit it to a test (yours or someone else's) before the beginning of Amanda's turn or overwrite it with Obscure Studies. You can also just power through, doing testless actions or throwing in more icons than usual. There are a few cards that might let you find and discard this, but usually Amanda would prefer to get rid of her Basic Weakness, since it's likely to be harsher than her signature. Once in a while, this weakness will catch you in a very bad place, but, most scenarios, it will be the lightest of speed bumps.

The discard condition: Discard it at the beginning of Amanda's next turn or overwrite it with her signature.

All in all, this is a way below average signature weakness.