What you have likely encountered is an exam-maker's intolerance for the split infinitive, i.e. the insertion of any word in a to-infinitive between to and the verb. To quickly clean is a split infinitive; a more famous example is the old Star Trek intonation to boldly go.
The original objection to the split infinitive came from early grammarians who wanted English to be more like Latin. There is no grammatical basis for calling it incorrect, however. Stylistically, too many intervening words can make the phrasing awkward, and since many people for many generations were taught that splitting an infinitive was always incorrect or a sign of poor writing, it can be a distraction regardless of its grammatical validity. Like starting a sentence with and or hopefully, or ending it with a preposition, splitting an infinitive is something a confident writer should feel free to do, but only if prepared to receive disparagement from more prescriptivist people.
The Chicago Manual of Style FAQ on split infinitives notes
CMOS has not, since the thirteenth edition (1983), frowned on the split infinitive. The sixteenth edition suggests, to take one example, allowing split infinitives when an intervening adverb is used for emphasis (see paragraphs 5.106 and 5.168). … [E]uphony or emphasis or clarity or all three can be improved by splitting the infinitive in certain situations.
The New York Times FAQ on Style, quoting their stylebook, notes
split infinitives are accepted by grammarians but irritate many readers. When a graceful alternative exists, avoid the construction… When the split is unavoidable, accept it: He was obliged to more than double the price.
