The advice given above is relevant to devices classified such that they require a
510k submission. Most class I devices don't require that.
If the device post-modification falls under a procode that doesn't require a 510k (again, most procodes under class I don't), then you don't have to worry about whether or not a 510k is required (or a note to file). All devices (including class I) are subject to the
General Controls. Based on the original device already being cleared (adequately, I presume, since FDA is not involved in pre-market clearance of most class I devices), the General Controls have already been applied and are continuously being maintained. As such, all that is required is continuation of practice as already established, including all provisions pertaining to device changes.
Some class I procodes are also GMP exempt, which means that the quality management system requirements are very limited. Even those that are not GMP exempt, are likely to be exempt from Design Control (21 CFR 820.30). The processes (and documentation) required by the regulations for device changes depend on the required level of quality system (GMP exempt / GMP without Design Control / GMP including Design Control). This would be defined by the applicable procode. It's essential to understand upfront what procode the device would fall under after the change.
Cheers,
Ronen.