LS7 filling the gaps image with google earth engine

You could try filling the gaps before you aggregate them by month.

USGS published a LS7 SLC-off gap-filling algorithm.

This algorithm was recreated for Google Earth Engine by Noel Gorelick: https://code.earthengine.google.com/d20cba5268ccbe117e2fc1c5fefc33f3

Building upon this Genadii Donchyts changed the algorithm for faster performance: https://code.earthengine.google.com/2ead14966758793579dfb31b94855275

The relevant thread can be found on the Google Earth Engine Developers messaging board (after registration).

For completeness, here is the relevant function from Noel Gorelicks Code:

var MIN_SCALE = 1/3;
var MAX_SCALE = 3;
var MIN_NEIGHBORS = 144;

/* Apply the USGS L7 Phase-2 Gap filling protocol, using a single kernel size. */
var GapFill = function(src, fill, kernelSize) {
  var kernel = ee.Kernel.square(kernelSize * 30, "meters", false)

  // Find the pixels common to both scenes.
  var common = src.mask().and(fill.mask())
  var fc = fill.updateMask(common)
  var sc = src.updateMask(common)

  // Find the primary scaling factors with a regression.
  // Interleave the bands for the regression.  This assumes the bands have the same names.
  var regress = fc.addBands(sc)
  regress = regress.select(regress.bandNames().sort())
  var fit = regress.reduceNeighborhood(ee.Reducer.linearFit().forEach(src.bandNames()),  kernel, null, false)
  var offset = fit.select(".*_offset")
  var scale = fit.select(".*_scale")

  // Find the secondary scaling factors using just means and stddev
  var reducer = ee.Reducer.mean().combine(ee.Reducer.stdDev(), null, true)
  var src_stats = src.reduceNeighborhood(reducer, kernel, null, false)
  var fill_stats = fill.reduceNeighborhood(reducer, kernel, null, false)
  var scale2 = src_stats.select(".*stdDev").divide(fill_stats.select(".*stdDev"))
  var offset2 = src_stats.select(".*mean").subtract(fill_stats.select(".*mean").multiply(scale2))

  var invalid = scale.lt(MIN_SCALE).or(scale.gt(MAX_SCALE))
  scale = scale.where(invalid, scale2)
  offset = offset.where(invalid, offset2)

  // When all else fails, just use the difference of means as an offset.  
  var invalid2 = scale.lt(MIN_SCALE).or(scale.gt(MAX_SCALE))
  scale = scale.where(invalid2, 1)
  offset = offset.where(invalid2, src_stats.select(".*mean").subtract(fill_stats.select(".*mean")))

  // Apply the scaling and mask off pixels that didn't have enough neighbors.
  var count = common.reduceNeighborhood(ee.Reducer.count(), kernel, null, true, "boxcar")
  var scaled = fill.multiply(scale).add(offset)
      .updateMask(count.gte(MIN_NEIGHBORS))

  return src.unmask(scaled, true)
}

var source = ee.Image("LANDSAT/LE7_L1T/LE70440342016075EDC00")
var fill = ee.Image("LANDSAT/LE7_L1T/LE70440342016027EDC00")