**Core Concept**
The child's presentation of recurrent respiratory tract infections, mouth breathing, and decreased hearing is suggestive of a congenital anomaly of the upper airway. This condition is often associated with adenoid hypertrophy, which can lead to nasal obstruction and subsequent mouth breathing, increased risk of respiratory tract infections, and hearing impairment due to Eustachian tube dysfunction.

**Why the Correct Answer is Right**
The correct answer is adenoidectomy, which involves surgical removal of the adenoids. This procedure is often performed in children with recurrent adenoiditis or adenoid hypertrophy, which can cause nasal obstruction, mouth breathing, and Eustachian tube dysfunction leading to hearing impairment. Adenoidectomy can help alleviate these symptoms by improving nasal breathing and reducing the risk of respiratory tract infections.

**Why Each Wrong Option is Incorrect**
* **Option A:** Antibiotics are not a suitable treatment for adenoid hypertrophy or recurrent respiratory tract infections as they do not address the underlying cause of the condition.
* **Option B:** Nasal decongestants may provide temporary relief from nasal obstruction but do not address the underlying adenoid hypertrophy or recurrent infections.
* **Option C:** Grommets (tympanostomy tubes) are used to treat otitis media with effusion (fluid in the middle ear) but do not address the underlying adenoid hypertrophy or recurrent respiratory tract infections.

**Clinical Pearl / High-Yield Fact**
It is essential to note that adenoidectomy should be considered in children with recurrent respiratory tract infections, mouth breathing, and hearing impairment, especially if they have a history of recurrent adenoiditis or adenoid hypertrophy.

**Correct Answer:** C. Grommets (tympanostomy tubes)