On 20a Rava explains that it's no problem if the wife pays the scribe's fees, for if we need we can assume that the rabbis conveyed the value she paid to the husband (under the principal hefker beit din haya hefker). Thus, it is essentially as if the husband owned the document.
Then on 20b we discuss the case of a tablet belonging to a woman, and the
husband writes the get on the tablet and brings it to the beit din. Rami bar
Chama asks if the woman has legally transferred the tablet to her husband.
The Gemara answers that even if she gave it to him intending to get it back,
it still counts as though it's his property when she gives it to him.
Why doesn't the Gemara just cite the same principal of hefker beit din haya
hefker when discussing the case of the tablet?
Tosfos writes that although the Chachamim were willing to re-appropriate the money which she had invested in the Sofer, they would not readily apply Hefker Beis Din on the tablet which was actually hers, totally.