What does Kundera mean by this line, towards the end of chapter 2 in The Unbearable Lightness of Being?
The copy of Anna Karenina under her arm amounted to false papers; it had given Tomas the wrong idea
(This answer is based on the Italian translation of the given book. The reliability of my answer depends, therefore, on the accuracy of the translation.)
In Italian, the phrase you addressed is translated as:
L'Anna Karenina che lei teneva sotto il braccio era la carta d'identità falsa con la quale aveva ingannato Tomáš.
Trying to rephrase it in my poor English, only for the sake of showing how the Italian translator wrote it:
The copy of "Anna Karenina" that she was holding was the false identity document that fooled Tomáš.
or something similar (again, this is a poor translation!).
To finally address your question, in my opinion (based, as said, on my Italian copy) the author here meant that she was deliberately bringing a copy of "Anna Karenina" with herself in order to make she appear, at Tomáš' eyes, different from what she was (or, at least, from what she showed up to be). In the context of the contrapositions that are fundamental in Kundera's book, she tried to appear different from what she actually was, fooling Thomáš.