No, the US was not paying Germany during the WWI for Mauser patents used in Springfield M1903 rifle.

Licensing agreement for the use of Mauser patents has been reached in 1905 and stipulated that payments for rifles and stripper clips produced will not exceed $200 000. That sum was reached in 1909 and the US was free to produce more rifles without paying more to patent holders.

There was also a lawsuit about the usage of "spitzer" (pointed) bullets. The position of the US legal representative was that the US had experimented with spitzer bullets before DWM (parent company of Mauser) filed for a patent. That lawsuit was never concluded because it was still ongoing when with the start of the war Office of Alien Property Custodian seized the patent. The question of priority in spitzer bullet design was not properly litigated, yet the fact of seizure was deemed unlawful by a post-WWI court decision, which ordered a compensation of $300 000 to be paid to DWM for the patent.

While we can see that the US paid substantial amounts of money to Mauser and DWM all of the transfers were either well before the war or after it.