In the book Sri Krishna Temple At Udupi by B.N. Hebbar available for free download here: https://archive.org/details/SriKrsnaTempleAtUdupi/page/n55/mode/2up?q=kukke
the author says, I quote:
// Page n55
During the course of Madhva’s tours within Tujunad in these two decades, he once journeyed to the Kukke-Subrahmanya-ksetra, the second holiest spot in the ParaSurama-ksetra, located on the banks of the Kumaradhara river in the Sulya taluk of Tujuva. Here, he is said to have encountered one Narasimha Tlrtha, the abbot of a Smarta-Bhagavata sampradaya institution, who challenged the acarya to a verbal duel. Madhva is said to have worsted this Bhagavata sampradaya abbot and won the latter’s institution as a booty for emerging victorious in the dialectical encounter. Madhva is then said to have converted that institution into an apostolic center of his own sect which goes by the name Kukke-Subrahmanya Matha today.71 The background and details of this episode (i.e., Madhva’s visit to Kukke-Subrahmanya) are given in Appendix I of this thesis, while narrating the foundation of the Kukke Subrahmanya Matha.// Unquote.
From this one can see that the original character of that Temple was converted by Madhva upon the above episode. Madhva is said to have installed a Saligrama there, thereby making the conversion of the Shaiva/Smarta temple to a Vaishnava sectarian one.
This Saligrama installing there is stated by Wilson too in his 'A sketch of Religious Sects of the Hindus' p. 93:
Quote //It seems not improbable, that the founder of the Mddhwa sect was,originally, a Saiva priest, and, although he became a convert to the Vaishnava faith, he encouraged an attempt to form a kind of compromise or alliance between the Saivas and Vaishnavas. Ma'dhwa was first initiated into the faith of Siva, at Ananteswar, the shrine of a Linga, and one of his names, Ananda Tirt'ha, indicates his belonging to the class of Dasnami Gosains, who were instituted by Sankara'cha'rya ; one of his first acts was to establish a Sdldgram, a type of Vishnu, at the shrine of Subrahmanya, the warrior son of Siva,// unquote.