KSB defended itself after it was revealed that the wife of its chief executive Derek Robertson landed an executive post at the charity.
It has now been confirmed that the Office of the Scottish Charity Regulator (OSCR) has received a complaint about KSB.
The body is also under scrutiny over its acquisition of a trademark that bears the same name as a firm owned by the married couple.
KSB is a prominent environmental charity that receives over £15 million of its budget from Government.
However, the charity has been questioned over the process by which the CEO's spouse, Catherine Gee, found work there.
A month after Robertson took over last year, Gee secured an untendered consultancy at the charity.
She was then given a fixed-tem contract, after which she got the full-time post of "head of corporate services".
The job was not externally advertised and Gee was the only internal applicant.
Gee's "executive team" post was one of two senior roles filled this way at the time, and the charity said Robertson played no role in his wife's appointment.
It then emerged Gee had landed a top job at a charity previously led by Robertson, Groundwork Merseyside.
The revelations prompted SNP MSP John Wilson to write to ministers demanding an investigation, on the basis that the bulk of the charity's resources come from the taxpayer.
Although OSCR has also received a complaint, a spokesman for the organisation declined to elaborate on its substance or whether an investigation would be launched.
The charity is also facing questions about it taking on a trademark called "Give Green".
It is understood the trademark is the basis of a new "concept" being planned by KSB.
However, "Give Green" is also the name of a firm owned jointly by Robertson and Gee.
The company was incorporated in March 2010, around a year before the duo started at KSB.
The firm is listed as "non-trading", but has not been wound down.
Further details have also emerged about the hiring policy that led to Gee getting the corporate-services post.
The charity stated that its approach is to hire internally first and, if that proves unsuccessful, to allow external applicants.
It has now been established that this policy is not written down, but is simply an "accepted process" at KSB.
Wilson said: "I have written to Cabinet Secretary Richard Lochhead to request an investigation into the appointment of Derek Robertson's wife as a senior member of staff within the organisation.
"The latest revelation that KSB has the trademark for 'Give Green' raises further questions about whether the board has any oversight into the way in which the charity is operating."
Labour MP Graeme Morrice said: "I think there are questions about the hiring practices at the publicly funded Keep Scotland Beautiful. I also think it looks odd that KSB acquired a trademark that has the same name as a firm co-owned by the chief executive."
A KSB source said: "Anyone can make a complaint to OSCR on a whim and without reason or cause. We don't know who has made it, we don't know what it's about, but we are completely confident it will come to absolutely nothing."
Regarding the trademark "Give Green", the source said: "It's a concept. It's not live; it's never been live. KSB is still deciding whether and how to integrate it into its range of activities."