Is it possible to retrieve any sound from laptop speakers which has been cancelled unintentionally while recording from a microphone in Windows 7? I left the option to remove speakers' "background noise" checked by mistake. It seems to me that it is not possible but I would like to have a second opinion. Thank you.
No. The summing/cancellation/noise reduction was done before the source went to 'tape'. The is no 'pre-cleaning' or diff file to go back to. Most 'smart' or AI processes are designed to remove noise not add, so there is no specialist suite of tools to aid you in reversing this process.
There is the vague hope that there may be some small remnant of this signal which may be boosted after the fact, as a separate file. Some noise-reduction software will let you flip to hear what is being removed, as opposed to the result of removal. There may be some small mileage in taking this & seeing what you can gain from it.