In order for me to properly assess what you have I will need to see images of the trivet and clear, in-focus close-ups of the mark.
Please send the photos at your convenience. There is not an extra charge to provide more pictures here.
I am wondering if you are still interested in having your item assessed?
Please let me know and do you have requested images available?
I look forward to reading back from you.
I have not yet received photos of your Rookwood tile, however the aberration of the mark may be that this is a late 20th century Townley tile. The Townley's purchased the rights to reproduce wares from Rookwood molds in the 1980's.
Here is a link for you on the history of such:
Please let me know if I can be of further assistance or if you are able to send images.