Need some simple vector help

I have a handful of logos that were probably made with ai. I am needing to turn them into vectors. Image trace leaves a mess and lots of work after. i did take graphic design 1 3 years ago but need some help please

Organization Mission

To coordinate charitable efforts, extend Christian compassion, and advocate for affiliated ministries while caring for neighbors through charitable endeavors and acts of kindness in accordance with the gospel of Christ—bringing glory to Christ and ensuring the faith-based community is a cornerstone of care for vulnerable populations.