Googling "1-methyl 3'-pseudouridine" brings up 14 hits not all actually containing the term and some on facebook. I think this refers to N1-methylpseudouridine.
From a EU report on Moderna's vaccine:
The RNA contains modified N1-methylpseudouridine instead of uridine to minimise the indiscriminate recognition of the mRNA by pathogen-associated molecular pattern receptors (e.g. TLRs
There's a paper that also suggests that's in Pfizers vaccine.
Googling it + FDA doesn't show any discussion that you would likely see if it's the reason that the FDA rejected other approval.
The fact that the substance naturally occurs in mammal also suggests that it's not toxic and mammals can handle it generally.