No, I would not be concerned about that tiny little bit. The max recommended dermal (skin) use level for sweet birch EO is around 2.5% according to Essential Oil Safety, Tisserand and Roberts, 2nd ed. It's not recommended for internal use. It's also not recommended for use by pregnant women. All in all, I have chosen to not use it at all, but that's my personal choice. I have occasionally used skin balms with this EO in them, and think infrequent, spot use is fine.
Birch EO contains a high % of methyl salicylate, which is an anticoagulant. Wintergreen EO is another one with a high % of salicylate, but we use small amounts of wintergreen EO to flavor mints and other candies. Wintergreen EO has a max dermal use level of 2.4% according to Essential Oil Safety.
You would want to avoid using any EOs high in salicylate when also using any kind of anticoagulant drug such as aspirin or blood thinner medication or if you bleed or bruise easily for whatever reason or if you have recently had surgery.
Most of the horror stories about this EO happen when people use an excessive amount of the EO on their skin for a long time or choose to take it internally. EOs with high levels of salicylate often used in salves used for soothing sore muscles, and some people become compulsive about using warming/soothing skin balms as other people are about using lip balms every few minutes. Other people get into serious trouble when they ingest the EO or use the EO while also taking other preparations or medications that inhibit blood clotting.