Mary is a pretty classic character – the pushy maid. Let's see what are some examples? Rosie from The Jetsons, Florence from The Jeffersons, and, let us not forget, Alice from The Brady Bunch. This character type actually goes even further back – check out Dorine in Moliere's 1664 comedy Tartuffe, if you don't believe us. The "clever servant" was also a stock character in the Commedia dell' Arte, an improvisational form of theatre from the Italian Renaissance. The earliest examples of this character type actually appear in Greek and Roman comedies. So, yeah, Ionesco's Mary the Maid is in some pretty old school company.
Our buddy, Mary, bears all the trade-marks of many of her pushy maid counterparts. For one, she doesn't seem to know "her place." When the Martins first enter, she fusses at them for being late. And, of course, she challenges the status quo by daring to recite a poem in the presence of the Smiths and their guests. She also challenges social norms by declaring her past relationship with the Fire Chief and throwing herself into his arms. Mary also seems to be in on some information that her "betters" don't know about, at least in regards to the Martins' true identity. She reveals to the audience that, though the Martins think they're husband and wife, in actuality they aren't.
Though Mary exhibits lots more personality than either the Smiths or Martins, she's still in many ways just as generic. As we've pointed out her character type has been around for a long, long time. Just like with his dialogue, Ionesco creates in Mary a sort of mutated cliché.