Supplement fee Mt Fuji Ltd Express

The fastest method is to take the Mount Fuji Limited Express from Odakyu Shinjuku Station to Gotemba Station and transfer to the free shuttle bus to the outlets. The trip takes around 100 minutes and costs about 2800 yen. Since this train partly travels over non-JR railway tracks, Japan Rail Pass holders must pay a supplement fee when using this train.
The question is :
1. Is it a direct train from Shinjuku Station to Gotemba Station (no transfer?)
2. How much does a JR Pass holder must pay for the supplement fee for this trip.
Thank you.

This is not the MT Fuji express.

It is the romance car.

https://www.odakyu.jp/english/romancecar/surcharges/

1. It is a direct service.

2. Very little of the 95 minute journey is on JR lines, expect to pay almost all of the 2810 yen.

The OP is not talking about the Romance Car, but the train to JR Gotemba (LTD. EXP. MT.FUJI).

As start and end are both JR stations, I am not sure there is a surcharge on that particular route - it would be pretty small.

Hmmm, different definitions/names for the trains so the Mt.Fuji Limited Express may also be "romance" car - probably because they use similar rolling stock. The hyperdia routing doesn't differentiate when restricted to JR trains, but the Gotemba outlet site does have a useful access page detailing JR travel options which show JR routes that wouldn't cost extra if using a rail pass.
https://www.premiumoutlets.co.jp/en/gotemba/access/train/