Hu, Li and Yang's conjecture on rainbow triangle tilings

Let $G$ be an edge-coloured graph on $n$ vertices, and let $k$ be a positive integer. The colour degree $[?]$ is denoted by $[?]$.

Hu, Li and Yang's conjecture. If

$$\delta^c(G) \geq \frac{n+k}{2},$$

then $G$ contains a rainbow-$K_3$-tiling of size $k$.

This conjecture asks for the minimum colour-degree threshold forcing a prescribed number of vertex-disjoint rainbow triangles. The source gives no resolution status.