The clip was made by or for Remington, for use in the Model 8 and the Model 81 self-loading rifles. There were six different clips. Four of them look much like the one you have, while two others were made of steel and were absolutely flat on the bottom. Your narration is incorrect only in that you say the clip is marked for the .30 Remington and .300 Savage. that would not be the case, and your picture shows it was for the .35 Remington and .300 Savage. One variant was marked only for the .35 caliber, with no mention of the Savage caliber. The .35/.300 clip was sized differently. by necessity due to cartridge dimensional differences, than those for the .25, .30 and .32 Remington, those three calibers taking the same clip.
While the Remington Model 30 might work with these clips, if the Model 30 had the same clip loading slot as the Model 1917 Enfield, there would have been no need to make a special, new type clip, as the Model 1917 was designed for the standard U.S. Military charger originally designed for the Model 1903 Springfield, for obvious reasons of combat interchangeability. Remington could simply have provided surplus .30-06 chargers, or new ones made up for them. Some of the early target-shooting accessory dealers had new Springfield clips made up for the match shooters using the NM version or N.R.A. versions of the Springfield.
Remington’s 1906 catalog indicated that rifles came with three clips, but others were available from Remington for a dime apiece. In the 1920s, the clips were listed as Part G298 Clips, for 20 cents apiece, and you were advised to specify the caliber, so there was not a separate part number for the two clips for the two different cartridge head sizes. In the 1951 catalog, the part number was 495, cartridge clip assembly 30-32 Remington, and Part 490 for the 30 Remington and 300 Savage, and they cost 95 cents each.
It is the opinion of the author of the below-cited reference that these clips do not make loading of Model 8 and Model 81 Remington rifles any easier, and warns of possible finger pinching in using them. I have no opinion on that issue, as although I once owned a 35 Model 81 Remington, it kicked too hard for its usefulness, and I sold it. I never had a clip to try it with.
The above is only a summary - more information about the clips and their variations is in the cited reference.
Reference: “The 8 and The 81, A History of Remington’s Pioneer Autoloading Rifles,” revised Second Edition, by John Henwood.