Tosefta do Tohorot 2:10

There is a stringency with an olive's bulk from a corpse, which is that an olive's bulk from a corpse, an opening of a handbreadth [is enough to prevent the spreading of impurity], whereas [an entire] corpse [requires] an opening of four handbreadths [to prevent the spread of impurity] (see Oholot 3:6). Rabbi Natan says, one who possesses corpse-impurity can impart second-degree impurity, and can disqualify [terumah] at an additional degree (i.e., third-degree impurity, see Toh. 2:8).

A person gives [his produce] to an innkeeper to cook a dish for him, and she puts down the pot in front of him, and empties out its contents (see Toh. 2:1 ("מְנַעֶרֶת אֶת הַקְּדֵרָה")), even [if she is a] Gentile, there is no need for concern. (Cf. Dem. 3:5.)