What was the only thing that Hanuman begged to Lord Shiva?

They are not considered as manifestation of master Shiva

Going to the Answer for this Question (intriguing truth story)

There is a sanctuary called Kundala Karaneswarar Temple, were Hanuman asked Lord Shiva and did repentance to get back his tail which is isolated from his body ,

This sanctuary committed to master shiva and his associate Bala tripura sundari (Parvati)

In Ramayana subsequent to overcoming Ravana, Sriram arrived at Rameswaram, on his approach to Ayodhya. As he slaughtered Ravana, he was gotten by Brahmahatya Dhosha. One will experience the ill effects of this Dhosha, on the off chance that he slaughters a Brahmin. Ravana, however being an evil spirit ruler, was a Brahmin as he was destined to a Rishi. Sriram was prompted by His Guru Sage Vashistha to get a shiva Lingam from Kaasi (varanasi)and perform poojas to Lord Shiva to get eased from the Dhosha, with the goal that he can continue to Ayodhya to assume responsibility as the ruler. Master Rama accepted his Guru's recommendation and sent Anjaneya Hanuman to bring a Shiva Lingam from Kaasi Kshethra. Ruler Anjaneya took the request for his lord and went to Kaasi and brought a Shiva Lingam.

Ruler Hanuman and jatayu looked all over before discovering one in Northern India, close to introduce day Kashi. Anyway they thought that it was hard to get their hands onto the lingam as it was monitored by Lord kala bairav, A fight resulted between ruler Hanuman and kala bairav with the previous at last predominant.

Back in Rameshwaram, time was running out. With no indication of master Hanuman or Jatayu , ruler Rama encouraged his partner Sita to set up a lingam out of the ocean sand close by. She did as such, and this was utilized for the compensation ceremonies.

As the ceremonies were finding some conclusion, ruler Hanuman was located with the lingam close by.

Nonetheless, on seeing that the ceremonies were finished without his quality, he was incredibly disillusioned. He gave winning a shot Sri Ram to utilize the lingam acquired by him, for the ceremonies, rather than the one developed by maa Sita. In an offer to pacify him Sri Ram recommended that if that somehow managed to be done, ruler Hanuman would need to clear out the lingam built by sita and spot the lingam brought by him, in its place.

As hard as ruler Hanuman attempted, he was unable to move the lingam. At last he attempted to fold his tail over it and yank it off the ground. The power he applied was extraordinary to the point that the lingam got removed, yet handled a couple of miles from Rameshwaram in a spot called ruler Hanuman pallam(pit made by Lord Hanuman). Simultaneously, his tail got isolated from his body.

Ruler Hanuman understood his imprudence. It was pre-appointed that the lingam arranged by Sita was to be utilized for the customs and looked for absolution from master Ram and maa Sita to regrow his tail.

Sriram blew up because of disregard to his Shivlinga by master Hanuman, and subsequently recommended ruler Hanuman to look for absolution from ruler Shiva just rather, and proposed that ruler Hanuman to visit Thirukurungaval and love Lord Shiva there to get back his tail. Thus the spot has procured its name, Tirukurunkaval (Place where Lord Shiva was loved by a monkey-confronted God) and did atonement of master Shiva , at long last ruler Shiva and his associate goddess Tripura Sundari (Parvati)appeared favor him to get back his tail

The declaration to this story is that it is one of only a handful hardly any Lord Shiva sanctuaries on the planet, with an altar to Hanuman confronting Shiv Linga rather than Nandi.

Also Read- Does anyone know the real strength of Hanuman?