Step 1) Pick basic wings torus knot.
Step 2) LOOK into it to see the overhand knot.
Step 3) Cut away the parts that you don't want in your overhand knot.
Step 4) Extrude the two tethers or strings coming out of the knot.
Step 5) Select edge rings and make them fatter for tight knot.
Add a step 3b) If you want to re-align a few edge loops as you extrude.
Sight, but we need some tweak in order to get a tight knot with a minimum of overlapping faces:
the bottom images were after apply edge loop/edge ring and scale uniform to make the "rope" thick and get the knot tight.
Please, correct me if I did the wrong steps. Pictures/videos are welcome to "How To" threads (mandatory should be the word).
Seems like you picked a bad place to cut your knot before extrude. I would offer that maybe a careful magnet move via the extruded edges might recenter then to avoid unwanted overlaps. Don't have time to share more than words today.
I'm advocating that the end user may not care too much about either a little gap space ... or ... a little overlap. My How to was listed in 5 steps ... which DO HELP.