Is it obligatory for girls and women to conceal the lines of their hands when writing to non-mahram men out of modesty, and were the Salaf keen on doing so?

A woman is not obliged to conceal her handwriting from non-mahram (definition) men. There is no evidence in Islamic law that commands this, nor is it known that the Companions, the Salaf (pious predecessors), or the Imams required their wives or daughters to do so. On the contrary, the women of the Salaf used to write Hadith (definition) and knowledge, and both men and women would examine it without any objection. Examples have been reported of virtuous women who wrote with beautiful and distinguished handwriting. Islamic law forbade women from speaking in a submissive manner, adorning themselves, wearing perfume, or speaking unnecessarily in front of non-mahram men, but not from merely their handwriting.