The orcidlink package itself doesn't provide direct options for controlling the link's appearance. However, since orcidlink internally uses the hyperref package, you can control the link appearance using hyperref options.
You need to add "\usepackage[hidelinks]{hyperref}" before "\usepackage{orcidlink}" to disable the colored box around the orcid link.
\usepackage[hidelinks]{hyperref}
\usepackage{orcidlink}