Have any pseudo-anglicisms become proper English words?

There are plenty of pseudo-anglicisms in other languages around the world: Handy, Pullunder, Showmaster and Beamer¹ in German. These words, though borrowed from English, are used differently from their usual English meanings. Have any pseudo-anglicisms later become common English words?

^{¹ I’m mentioning Beamer (German word for projector) especially as there is a popular package for the LaTeX typesetting system that helps in creating projection slide; such uses could potentially spread a pseudo-anglicism.}

From Wikipedia: "Pseudo-anglicisms are related to false friends [hyperlinked] or false cognates [hyperlinked]. Many speakers of a language which employs pseudo-anglicisms believe that the relevant words are genuine anglicisms and can be used in English, which may cause misunderstandings. When many English words are incorporated into many languages, language enthusiasts and purists often look down on this phenomenon, terming it (depending on the importing language) Denglisch, Franglais or similar neologisms."

From Lloyd James' website (http://www.lloydbingham.co.uk/2013/02/top-5-pseudo-anglicisms-in-german.html) come the following pseudo-anglicisms:

downloader, streetworker, talkmaster, know-how, wellness, and beamer.

Of interest to readers of EL&U:

Wellness: "Germans will associate this word with being pampered at a Wellness-Hotel, perhaps in the secluded mountains of Austria where one can enjoy the utmost tranquility and relaxation. In English, we could probably just call this a spa." Streetworker: "The meaning of streetworker [the "real" English word being streetwalker!]is more innocent in German [than English], referring to a social worker rather than a lady who was the object of the 1978 single Roxanne by The Police."

In answer to your question, I am familiar with only one anglicism, and that is the Japanese/English term Walkman, which was a popular medium of portable music decades ago that featured a pint-size combination AM/FM radio and cassette player--with headphones (or ear-buds), of course.

anime

The Japanese borrowed the English word animation, abbreviated it to anime and used it to refer animated movies and videos.

The English then took the word anime back, and used it to refer specifically to Japanese animated movies and videos.