A mirror twin-domain boundary (MTB) in monolayer MoSe2 represents a (quasi) one-dimensional metallic system. Its electronic properties, particularly the low-energy excitations in the so-called 4|4P-type MTB, have drawn considerable research attention. Reports of quantum well states, charge density waves, and the Tomonaga-Luttinger liquid (TLL) have all been made. Here, by controlling the lengths of the MTBs and employing different substrates, we reveal by low-temperature scanning tunneling microscopy/spectroscopy, Friedel oscillations and quantum confinement effects causing the charge density modulations along the defect. The results are inconsistent with charge density waves. Interestingly, for graphene-supported samples, TLL in the MTBs is suggested, whereas that grown on gold, an ordinary Fermi liquid, is indicated.