The following word uses an extra letter not found in the main word is: RELATIONSHIP

Correct — D.
Rule: an option may use a letter only as often as the main word has it.

RELATIONSHIP: R, E, L, A, T, O, N, S, H, P once each, and I twice.
THRILLS needs two L's, and RELATIONSHIP has a single L.
That second L is the extra letter → option (d).

Why the others are wrong

• (a)
  POSHER — POSHER uses P, O, S, H, E and R once each, and RELATIONSHIP has every one of them. Nothing is extra.
• (b)
  EARTH — EARTH uses E, A, R, T and H once each, all present in RELATIONSHIP, so no letter is extra.
• (c)
  POLISH — POLISH uses one L and one I. RELATIONSHIP has one L and two I's, so every letter is covered.

Word-formation items check letters with their counts. List the main word's letters with how often each appears, then test each option letter by letter, crossing a letter off as you use it.

Every letter of THRILLS, that is T, H, R, I, L and S, appears in RELATIONSHIP. What fails is the count: THRILLS uses L twice, and RELATIONSHIP has a single L to give.

Key facts

• RELATIONSHIP has 12 letters: R, E, L, A, T, O, N, S, H, P once each, and I twice.
• THRILLS has 7 letters, with L twice.
• An option that repeats a letter more often than the main word does cannot be formed from it.

Common traps

• Checking only whether each letter appears, and missing that THRILLS needs L twice
• Crossing out letters from memory instead of writing the main word's letter counts down

No directly related past PYQ was found.