Bill, in Pro+, you can just Round Corners. It takes 2 seconds.
In earlier versions, create a Curved Corner Rectangle, adjust size and curvature then Fill > Bitmap.

The KalTire site actually has a good PNG already: https://www.kaltire.com/on/demandwar...NHL-Lockup.png
You could remove the extra detail easily and gain a crisp 1500px wide image at 96dpi.
Yes, you would need to overlap the R roundel with a TM one.
It the light Grey was required, instead of White, you could overlay a grey rectangle and add a Multiply Transparency.

I probably would just create a Black curved corner rectangle with a 1-step inner contour and set the inner to light grey.
For the lettering, if there is a font, use that.
If not, build the lettering from skewed rectangles for I, L, T & E. As you gain proficiency, do A & K and finally R.
Trace these out with the Shape tool, but make them non-italic then skew.

Acorn