I found the following entries on Wiktionary (emphasis mine):
carte
French
noun
- card
- chart; map
- menu
card
English
From Middle English carde (“playing card”), from Old French carte, from Latin charta, from Ancient Greek χάρτης (khártēs, “paper, papyrus”).
chart
English
From Middle French charte (“card, map”), from Late Latin charta (“paper, card, map”), Latin ("papyrus, writing"), from Ancient Greek χάρτης (khártēs, “papyrus, thin sheet”).
χάρτης
Ancient Greek
noun
- sheet of paper
- book
From χαράσσω (kharássō, “I scratch, inscribe”), from Proto-Indo-European *ǵʰer- (“to scratch”).
scratch
English
Probably from a blend of the Middle English words scratten (“to scratch”) and crachen (“to scratch”).
I couldn't find any further etymology for scratch. It seems to me that Ancient Greek χάρτης (khártēs) is similar to Modern English scratch (e.g. a mid-point could be krats). Could these words have the same source as each other considering that the root word is hypothesised to mean scratch?