how to remove all the small islands from the Census Shapefile (zip code level)?

I have downloaded the Census shapefile at the zip code level, cb_2017_us_zcta510_500k.shp (https://www.census.gov/geo/maps-data/data/cbf/cbf_zcta.html)

I also have downloaded the mapping file that allows me to add the corresponding STATE variable (https://www.census.gov/geo/maps-data/data/zcta_rel_download.html)

I merged the two and I get:

library(sf)
library(dplyr)

big_df 

Simple feature collection with 44434 features and 2 fields
geometry type:  MULTIPOLYGON
dimension:      XY
bbox:           xmin: -176.6847 ymin: -14.37374 xmax: 145.8304 ymax: 71.34122
epsg (SRID):    4269
proj4string:    +proj=longlat +datum=NAD83 +no_defs
First 10 features:
   ZCTA5CE10 STATE                       geometry
1      35442     1 MULTIPOLYGON (((-88.25262 3...
2      35442     1 MULTIPOLYGON (((-88.25262 3...
3      35442     1 MULTIPOLYGON (((-88.25262 3...

Now, I tried to filter all the small islands and Alaska:

remove_list <-  c("02", "15", "72", "66", "78", "60", "69",
"64", "68", "70", "74", "81", "84", "86", "87", "89", "71", "76",
"95", "79")



big_df %>% filter(!STATE %in% map(remove_list, as.integer)) %>% 
  tm_shape(.) + tm_polygons('pt_count',palette = "Reds", 
                            style = "quantile", n = 10, 
                            title = "counts") 

but I still get some tiny islands.

What am I missing here? Thanks!

Here is a way of obtaining the geometry (country outline) for mainland US:

library(raster)
library(sf)
library(dplyr)

us = getData('GADM', country='USA', level=0) %>%
  st_as_sf() %>%
  st_cast("POLYGON") %>%
  mutate(area = st_area(.)) %>%
  arrange(desc(area)) %>%
  slice(1) # mainland US should be the largest

You can then use this to run st_intersection(big_df, us) to extract only the parts of big_df within us. Note that it may pay off to first create a st_buffer or st_convex_hull around us to ensure your big_df doesn't get clipped somewhere along its borders.