Mishnah 7 in chapter 11 of Maseches Terumos is a direct continuation of the previous mishnah, and it even opens with the word "vechein" - to teach us that the very same principle applies here as well. In the previous mishnah we learned that a storeroom which had held wheat of Terumah need only be swept out well, and the owner is not required to sit on the floor and pick out every last crumb of Terumah that may have remained in it before bringing unconsecrated produce inside.
The case before us:
A storage vessel that had oil of Terumah inside it - a barrel, for example - and the oil was poured out of it. The question is how careful a person must be with the oil left on the walls of the barrel after it has been emptied.
The wording of the mishnah: "vechein chavis shel shemen shenishpechah" - a barrel that had held oil of Terumah, and now the oil has been poured out and has left it. Regarding this the mishnah rules: "ein mechayvin oso letapei'ach" - we do not obligate the owner to sit on the ground and wipe down the walls of the vessel in order to clean it thoroughly.
The Bartenura's explanation of the word "letapei'ach":
The Bartenura understands that "metapei'ach" comes from the word "tefach" - the width of the palm; that is, that a person should take his hand and wipe the walls of the vessel with his fingers. It is worth noting: the possibility of cleaning it with a rag never even entered the Bartenura's consideration, and even wiping with the hands alone is not required.
The mishnah concludes: "ela noheig bah kederech shehu noheig bechulan" - he treats this barrel the way he treats barrels of wine that are not Terumah: he pours out the contents, and from the moment he has poured it out it is considered empty. And as for the little that remains on the walls - that is of no consequence.
In summary: in this mishnah we learned that the law of the storeroom in the previous mishnah applies equally to a vessel that had held oil of Terumah: we do not obligate a person to wipe down the walls of the vessel and clean it thoroughly, not with a rag and not even with his hands, but rather he treats it the way one treats any barrel - emptying out its contents, and nothing more.