JavaScript (ES6), 69 bytes

Expects (set)(string).

s=>g=([c,...b],o='',[p,,q]=o)=>q?s.has(q+p):c?g(b,o)+(c>o)*g(b,c+o):0

Try it online!

Commented

s =>            // s = set of letter flagsg = (           // g is a recursive function taking:  [ c,          //   c = next character from the landscape      ...b ],   //   b[] = array of remaining characters  o = '',       //   o = string of selected letters, in reverse order  [ p,,         //   p = 1st character of o        q ] = o //   q = 3rd character of o) =>            //q ?             // if q is defined:  s.has(q + p)  //   increment the result if q + p exists in s:               // else:  c ?           //   if c is defined:    g(b, o) +   //     do a recursive call with o unchanged    (c > o) *   //     the 2nd call is valid only if c > o    g(b, c + o) //     do a recursive call with c + o  :             //   else:    0           //     stop the recursion

Python 3.8, 85 bytes

I was curious to see if a port in Python could compete with user1609012's answer.

Thanks to @tsh who managed to save 4 bytes.

f=lambda s,a,o="":o[::-2]in a or s>""==o[2:]and(s[0]>o)*f(q:=s[1:],a,s[0]+o)+f(q,a,o)

Try it online!