Lord Lyon Sir Thomas Innes of Learny writing in 1934 (Scots Heraldry) had this to say regarding "clan badges":

"The use of this so-called 'garter' has been criticised* as (1) an infringement of the privilege of Knights of the Garter; (2) a breach of the Laws of Arms. Investigation shows that the long-standing Scottish practice is strictly correct. In Lyon Register the 'garter' has been officially described as a 'belt and buckle', and the popular Scottish cap-badge is simply a conventional form of the plate and strap with which clansmen and adherents bore their Chief's badge. The use of a Chief or Chieftain's badge in this form is therefore not a "usurpation of arms', but an expression of adherence to that particular Chief or Laird."

(*This criticism was on-going from from the College of Arms in London. -- MoR)

Whether the belt and buckle (also, and in my opinion more correctly, referred to as a strap and buckle) is tucked ("nowed" in heraldic terms) or looped is really down to the blazon. If not specified as nowed, then the belt/strap should be looped, not "tucked". Interestingly, in Innes of Learney's books, the clansman's badge is always depicted as "looped", which would lead me to believe that this is the "proper" way it should be depicted.

That said, one of the 20th century's greatest herald painters, Don Pottinger,
inevitably, and I do mean inevitable, depicted clan badges with the belt and buckle nowed. (It's Pottinger's artwork that appears on Lyon's website.) His protege, Romilly Squire of Rubislaw (another of the world's best herald painters) always depicts the strap and buckle as looped.

So which is correct? Looped. Unless the blazon issued by the granting authority says "nowed" (ie: knotted) then the only possibility is looped.